F4120 Theoretical mechanics

Faculty of Science
autumn 2021
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
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
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. 2nd ed. Oxford: Pergamon Press, 1969. vii, 165 s. info
  • BRDIČKA, Miroslav and Arnošt HLADÍK. Teoretická mechanika [Brdička, 1987]. 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 [Brdička, 1959]. 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. T. 1, Mechanika [Landau, 1973]. Moskva: Nauka [Moskva], 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
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020.
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