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PřF:F5510 Analytical mechanics - Course Information

## F5510 Analytical mechanics

**Faculty of Science**

Autumn 2018

**Extent and Intensity**- 2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
**Teacher(s)**- doc. Klaus Bering Larsen, Ph.D. (lecturer)

doc. Klaus Bering Larsen, Ph.D. (seminar tutor) **Guaranteed by**- prof. RNDr. Jana Musilová, CSc.

Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science

Contact Person: doc. Klaus Bering Larsen, Ph.D.

Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science **Timetable**- Mon 17. 9. to Fri 14. 12. Mon 17:00–18:50 F3,03015
- Timetable of Seminar Groups:

**Prerequisites**- Knowledge of elementary classical mechanics, electrodynamics and special relativity.
**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, N-FY)

**Course objectives**- The Lagrangian and Hamiltonian formalism in classical mechanics and relativistic field theory; variational principles; symmetry, conservation laws and Noether's theorems; Poisson brackets; canonical transformations; Hamilton-Jacobi theory; the canonical and symmetrical tensors of energy-momentum, connections between classical and quantum mechanics, the mathematical fundament of general theory of relativity. The main aim of this lecture is: to understand the formal basis of modern theoretical physics; to acquire connections between symmetries, conservation laws and equations of motion; to obtain ability to read contemporary physical literature.
**Syllabus**- Lagrangian formalism in the classical mechanics
- First theorem of E. Noether in the classical mechanics
- Lagrangian formalism in the field theory
- Connections between symmetries, conservation laws and field equations
- Second theorem of E. Noether
- Energy-momentum tensors
- Hamiltonian formalism, Poisson brackets, canonical transformations
- Hamilton-Jacobi equation
- Connection between classical mechanics, quantum mechanics and statistical physics
- Mathematical foundations of general theory of relativity

**Literature**- KRUPKA, Demeter.
*Lectures on differential invariants*. Edited by Josef Janyška. Vyd. 1. Brno: Univerzita J.E. Purkyně, 1990. 193 s. ISBN 8021001658. info - LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC.
*The classical theory of fields*. Translated by Morton Hamermesh. 4th rev. Engl. ed. Oxford: Elsevier Butterworth-Heinemann, 1975. xiii, 428. ISBN 0-7506-2768-9. info - LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC.
*Mechanics*. 2nd ed. Oxford: Pergamon Press, 1969. vii, 165 s. info

- KRUPKA, Demeter.
**Teaching methods**- two theoretical lectures, one exercise (solving problems)/a week
**Assessment methods**- credit for appropriate participation in the exercises; oral exam.
**Language of instruction**- English
**Further Comments**- The course can also be completed outside the examination period.

The course is taught annually.

- Enrolment Statistics (Autumn 2018, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2018/F5510