Course Information

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught in person.

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. Mgr. Tomáš Tyc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Prerequisites

F1030 Mechanics || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve problems from these areas.

Learning outcomes

The student will be, after finishing the course, able to: solve mechanical problems using Lagrange equations; identify integrals of motion in a given situation; analyse the problem of motion in the central potential; plot phase trajectories for simple systems; clearly explain the meaning of the tensors of stress, deformation and inertia and describe their propeties; solve simple problems of liquid flow and elastic body deformations.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught in person.

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. Mgr. Tomáš Tyc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Tue 12:00–13:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Thu 16:00–17:50 F4,03017
F4120/02: Mon 18:00–19:50 F4,03017

Prerequisites

F1030 Mechanics || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve problems from these areas.

Learning outcomes

The student will be, after finishing the course, able to: solve mechanical problems using Lagrange equations; identify integrals of motion in a given situation; analyse the problem of motion in the central potential; plot phase trajectories for simple systems; clearly explain the meaning of the tensors of stress, deformation and inertia and describe their propeties; solve simple problems of liquid flow and elastic body deformations.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught in person.

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. Mgr. Tomáš Tyc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Tue 11:00–12:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Tue 18:00–19:50 F4,03017
F4120/02: Mon 18:00–19:50 F2 6/2012

Prerequisites

F1030 Mechanics || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve problems from these areas.

Learning outcomes

The student will be, after finishing the course, able to: solve mechanical problems using Lagrange equations; identify integrals of motion in a given situation; analyse the problem of motion in the central potential; plot phase trajectories for simple systems; clearly explain the meaning of the tensors of stress, deformation and inertia and describe their propeties; solve simple problems of liquid flow and elastic body deformations.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught in person.

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. Mgr. Tomáš Tyc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Tue 11:00–12:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Tue 16:00–17:50 F4,03017
F4120/02: Wed 18:00–19:50 F3,03015

Prerequisites

F1030 Mechanics || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve problems from these areas.

Learning outcomes

The student will be, after finishing the course, able to: solve mechanical problems using Lagrange equations; identify integrals of motion in a given situation; analyse the problem of motion in the central potential; plot phase trajectories for simple systems; clearly explain the meaning of the tensors of stress, deformation and inertia and describe their propeties; solve simple problems of liquid flow and elastic body deformations.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught online.

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. Mgr. Tomáš Tyc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Tue 11:00–12:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Thu 15:00–16:50 F3,03015
F4120/02: Fri 14:00–15:50 F3,03015

Prerequisites

F1030 Mechanics || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve problems from these areas.

Learning outcomes

The student will be, after finishing the course, able to: solve mechanical problems using Lagrange equations; identify integrals of motion in a given situation; analyse the problem of motion in the central potential; plot phase trajectories for simple systems; clearly explain the meaning of the tensors of stress, deformation and inertia and describe their propeties; solve simple problems of liquid flow and elastic body deformations.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. Mgr. Tomáš Tyc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Tue 11:00–12:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Thu 17:00–18:50 F4,03017

Prerequisites

F1030 Mechanics || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve problems from these areas.

Learning outcomes

The student will be, after finishing the course, able to: solve mechanical problems using Lagrange equations; identify integrals of motion in a given situation; analyse the problem of motion in the central potential; plot phase trajectories for simple systems; clearly explain the meaning of the tensors of stress, deformation and inertia and describe their propeties; solve simple problems of liquid flow and elastic body deformations.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Mon 17. 9. to Fri 14. 12. Tue 11:00–12:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Mon 17. 9. to Fri 14. 12. Thu 18:00–19:50 F4,03017

Prerequisites

F1030 Mechanics || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Mon 18. 9. to Fri 15. 12. Wed 10:00–11:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Mon 18. 9. to Fri 15. 12. Mon 15:00–16:50 F1 6/1014

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Mon 19. 9. to Sun 18. 12. Wed 10:00–11:50 F2 6/2012

• Timetable of Seminar Groups:

F4120/01: Mon 19. 9. to Sun 18. 12. Wed 14:00–15:50 F4,03017
F4120/02: Mon 19. 9. to Sun 18. 12. Wed 16:00–17:50 F4,03017

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Wed 10:00–11:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Fri 16:00–17:50 F4,03017
F4120/02: Mon 17:00–18:50 F4,03017

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Wed 13:00–14:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Tue 16:00–17:50 F4,03017
F4120/02: Wed 17:00–18:50 F3,03015

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Wed 11:00–12:50 F3,03015

• Timetable of Seminar Groups:

F4120/01: Tue 17:00–18:50 F2 6/2012, F. Hroch
F4120/02: Wed 16:00–17:50 F3,03015, F. Hroch

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Tue 9:00–10:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Tue 16:00–17:50 F1 6/1014
F4120/02: Wed 18:00–19:50 F1 6/1014

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Tue 9:00–10:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Wed 18:00–19:50 F1 6/1014
F4120/02: Mon 16:00–17:50 F4,03017

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Tue 9:00–10:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Mon 15:00–16:50 F3,03015
F4120/02: Tue 16:00–17:50 F4,03017

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Tue 9:00–10:50 F3,03015

• Timetable of Seminar Groups:

F4120/01: Thu 18:00–19:50 F1 6/1014, F. Hroch
F4120/02: Tue 7:00–8:50 Fs2 6/4003, O. Přibyla
F4120/03: Fri 15:00–16:50 F3,03015, F. Hroch

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Tue 7:00–8:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Wed 17:00–18:50 F3,03015
F4120/02: Wed 15:00–16:50 F3,03015

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
RNDr. Jan Janík, Ph.D. (seminar tutor)
Mgr. Martin Netolický (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Tue 8:00–9:50 F4,03017

• Timetable of Seminar Groups:

F4120/01: Tue 16:00–17:50 F2 6/2012
F4120/02: Mon 15:00–16:50 F3,03015

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace (*). Pohyb jako kanonická transformace (*). Liouvillova věta (*). Hamiltonova-Jacobiho rovnice (*). Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace (*). Poissonovy závorky (*). Liouvillova věta (*). Hamiltonona-Jacobiho rovnice (*). B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Petr Dub, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Wed 8:00–9:50 F3,03015

• Timetable of Seminar Groups:

F4120/01: Mon 8:00–9:50 F3,03015, T. Tyc
F4120/02: No timetable has been entered into IS. T. Tyc

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanika a molekulová fyzika || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace (*). Pohyb jako kanonická transformace (*). Liouvillova věta (*). Hamiltonova-Jacobiho rovnice (*). Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace (*). Poissonovy závorky (*). Liouvillova věta (*). Hamiltonona-Jacobiho rovnice (*). B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Petr Dub, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Wed 7:00–8:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Fri 12:00–13:50 F4,03017
F4120/02: Mon 7:00–8:50 Fs1 6/1017
F4120/03: Fri 8:00–9:50 F4,03017

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physics || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace (*). Pohyb jako kanonická transformace (*). Liouvillova věta (*). Hamiltonova-Jacobiho rovnice (*). Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace (*). Poissonovy závorky (*). Liouvillova věta (*). Hamiltonona-Jacobiho rovnice (*). B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Petr Dub, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Timetable

Wed 9:00–10:50 F1 6/1014

• Timetable of Seminar Groups:

F4120/01: Wed 12:00–13:50 03039, T. Tyc
F4120/02: Fri 13:00–14:50 F3,03015, T. Tyc
F4120/03: Wed 7:00–8:50 03039, T. Tyc

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physics || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace (*). Pohyb jako kanonická transformace (*). Liouvillova věta (*). Hamiltonova-Jacobiho rovnice (*). Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace (*). Poissonovy závorky (*). Liouvillova věta (*). Hamiltonona-Jacobiho rovnice (*). B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Petr Dub, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physics || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace. Pohyb jako kanonická transformace. Liouvillova věta. Hamiltonova-Jacobiho rovnice. Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace. Poissonovy závorky. Liouvillova věta. Hamiltonona-Jacobiho rovnice. B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Petr Dub, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physics || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace. Pohyb jako kanonická transformace. Liouvillova věta. Hamiltonova-Jacobiho rovnice. Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace. Poissonovy závorky. Liouvillova věta. Hamiltonona-Jacobiho rovnice. B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Petr Dub, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanika a molekulová fyzika || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace. Pohyb jako kanonická transformace. Liouvillova věta. Hamiltonova-Jacobiho rovnice. Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace. Poissonovy závorky. Liouvillova věta. Hamiltonona-Jacobiho rovnice. B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Jan Horský, DrSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Zdeněk Bochníček, Dr.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jan Horský, DrSc.

Prerequisites

F1030 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

l.Space and time in Newtonian physics
2.Mechanics of particles systems
3.Principles of mechanics
4.Lagrangian formulation
5.Hamiltonian formulation
6.Rigid bodies
7.Basic tensors for continuous matter
8.Elastic contiuous matter
9.Equations of motions for continuous matter
l0.Viscosious liquid
ll.Relativistic point mechanics in the Minkowski space

Literature

• HORSKÝ, Jan and Jan NOVOTNÝ. Teoretická mechanika (Theoretical Mechanics). Brno: MU, 1998, 277 pp. ISBN 80-210-1990-5. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 4 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Jan Horský, DrSc. (lecturer)
Mgr. Milan Štefaník, Dr. (seminar tutor)

Guaranteed by

doc. RNDr. Zdeněk Bochníček, Dr.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jan Horský, DrSc.

Prerequisites

F1030 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Syllabus

• l.Space and time in Newtonian physics
• 2.Mechanics of particles systems
• 3.Principles of mechanics
• 4.Lagrangian formulation
• 5.Hamiltonian formulation
• 6.Rigid bodies
• 7.Basic tensors for continuous matter
• 8.Elastic contiuous matter
• 9.Equations of motions for continuous matter
• l0.Viscosious liquid
• ll.Relativistic point mechanics in the Minkowski space

Literature

• HORSKÝ, Jan and Jan NOVOTNÝ. Teoretická mechanika (Theoretical Mechanics). Brno: MU, 1998, 277 pp. ISBN 80-210-1990-5. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info

Language of instruction

Czech

Further Comments

The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Filip Hroch, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanics and molecular physic || F2060 Mechanics and molecular physic
The first year of Physics study should be completed successfully.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

Course of theoretical mechanics, a part of the course of theoretical physics.
Main objectives: to master the fundamentals of Lagrangian and Hamiltonian approaches to mechanics, to understand the basic mechanics of rigid body, theory of elasticity and fluid mechanics and to be able to solve simple problems from these areas.

Syllabus

• Hamilton variation principle, Euler-Lagrange equations, curvilinear coordinates, the form of Lagrange function.
• Conservation laws - cyclic coordinates, generalised energy, conservation of momentum and angular momentum of an isolated system, theorem of E. Noether.
• Integration of equations of motion - one-dimensional motion, motion in central potential, effective potential, Kepler problem, scattering of particles, cross-section, Rutherford formula.
• Hamilton canonical equations, canonical transformations, Poisson brackets, Liouville theorem, motion as a canonical transformation, Hamilton-Jacobi equation.
• Basics of rigid body mechanics - tensor of inertia and its diagonal components and deviations moments, angular momentum, rotational kinetic energy, motion of a spinning top, Euler equations.
• Theory of elasticity - displacement vector, deformation tensor, stress tensor, surface and volume forces, Hooke law for isotropic medium, equation of equilibrium for isotropic bodies.
• Hydrodynamics - the vector field of velocity, streamlines, tensor of velocity of deformation, vorticity, continuity and Bernoulli equations, equations of motion of fluids (Euler equations, Navier-Stokes equations).

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• JOSÉ, Jorge V. and Eugene Jerome SALETAN. Classical dynamics : a contemporary approach. 1st. pub. Cambridge: Cambridge University Press, 1998, xxv, 670. ISBN 0521636361. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Teaching methods

2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.

Assessment methods

Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

F4120 Theoretical mechanics

Extent and Intensity

2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
RNDr. Jan Janík, Ph.D. (seminar tutor)
Mgr. Martin Netolický (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Petr Dub, CSc.

Prerequisites

F1030 Mechanics and molecular physic || F1040 Mechanika a molekulová fyzika || F2060 Mechanics and molecular physic
The first year of Physics study should be finished

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives (in Czech)

Lagrangeovská formulace mechaniky. Hamiltonův princip nejmenší akce. Eulerovy-Lagrangeovy rovnice. Zákony zachování. Hamiltonovy rovnice. Kanonické transformace (*). Pohyb jako kanonická transformace (*). Liouvillova věta (*). Hamiltonova-Jacobiho rovnice (*). Základy mechaniky tuhého tělesa. Tenzor setrvačnosti. Mechanika malých kmitů. Zakladní veličiny pro kontinuum. Tenzor napětí a deformace. Rovnice kontinuity. Pohybové rovnice kontinua. Elastické kontinuum. Hookův zákon. Rovnice rovnováhy. Vlnění v kontinuu. Ideální tekutiny. Bernoulliho rovnice. Vazké tekutiny. Navierovy-Stokesovy rovnice.

Syllabus (in Czech)

• I. MECHANIKA HMOTNÝCH BODŮ A) Principy 1. Hamiltonův variační princip - Tvar Lagrangeovy funkce 2. Lagrangeovy rovnice - Vazby. Virtuální posunutí. Zobecněné souřadnice 3. Zákony zachování - Cyklické souřadnice. Integrál energie 4. Kanonické rovnice - Hamiltonovy kanonické rovnice. Kanonické transormace (*). Poissonovy závorky (*). Liouvillova věta (*). Hamiltonona-Jacobiho rovnice (*). B) Aplikace 5. Integrace pohybových rovnic - Jednorozměrný pohyb. Pohyb v centrálním poli. Keplerova úloha. Srážky částic - účinný průřez, Rutherfordův vzorec. 6. Pohyb tuhého tělesa - Eulerovy úhly. Tenzor setrvačnosti. Moment hybnosti a kinetická energie tělesa. Setrvačníky. 7. Malé kmity - Kmity soustav. Normální souřadnice. Kmity řetízku. Přechod ke kontinuu. Vlnová rovnice. II. MECHANIKA KONTINUA A) Teorie pružnosti 1. Tenzor deformace Vektor posunutí. Tenzor deformace. Malé deformace. 2. Tenzor napětí Plošné a objemové síly. 3. Hookův zákon Tenzor pružnosti. Krystaly a izotropní prostředí. 4. Termodynamika deformace Práce pružných sil. Vnitřní energie. Volná energie. 5. Rovnice rovnováhy izotropních pružných těles Jednoduché úlohy 6. Pohybová rovnice izotropního pružného tělesa. Vlny B) Hydrodynamika 7. Kinematika tekutin Pole rychlosti. Proudnice. Tenzor rychlosti deformace/rotace. Vírové a nevírové proudění. Cirkulace rychlosti. 8. Rovnice kontinuity 9. Pohybová rovnice - a) ideální tekutiny (Eulerovy rovnice, Bernoulliova rovnice) b) vazké tekutiny (Navierovy-Stokesovy rovnice)

Literature

• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
• HLADÍK, Arnošt. Teoretická mechanika. Edited by Miroslav Brdička. 1. vyd. Praha: Academia, 1987, 581 s. info
• GOLDSTEIN, Herbert. Classical mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1980, xi, 672 s. ISBN 0-201-02918-9. info
• BRDIČKA, Miroslav. Mechanika kontinua. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1959, 718 s. info
• LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Teoretičeskaja fizika. 3. ispr. i dop. izd. Moskva: Nauka, 1973, 207 s. info
• KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.

Listed among pre-requisites of other courses

• F5030 Introduction to Quantum Mechanics
  F4120 || F4050  
• F6040 Thermodynamics and statistical physics
  (F4120&&F4090)||(F4100)||(F4050)  

• Enrolment Statistics (Autumn 2024, recent)