MU:MU25008 Geometric Methods in Mechanics - Course Information

MU25008 Geometric Methods in Mechanics

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Guaranteed by

prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava

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

• Geometry and Global Analysis (programme MU, N1101)

Course objectives (in Czech)

Cílem přednášky je seznámení studentů se základy Poissonovy a symplektické geometrie.

Syllabus (in Czech)

• - Lagrangián a Eulerovy-Lagrangeovy rovnice. Symetrie a integrály pohybu. Věta Emmy Noetherove.
  - Poissonova závorka, Poissonovy a symplektické struktury na hladkých varietách, Darbouxova věta.
  - Hamiltonián, Hamiltonovská vektorová pole, Hamiltonovy rovnice.
  - Legendreova transformace a souvislost mezi Lagrangeovským a Hamiltonovským formalismem.
  - Integrály pohybu, úplná integrabilita a Liouvilleova věta.
  - Akce grup na Poissonových varietách. Zobrazení momentu.
  - Hamiltonova-Jacobiho rovnice, úplný integrál, separace proměnných, proměnné akce-úhel.
  - Bihamiltonovské systémy.

Literature

recommended literature
• R. Berndt. An Introduction to Symplectic Geometry. AMS, 2001. info
• V. I. Arnold. Mathematical methods of classical mechanics. Springer, New York, 1999. ISBN 0387968903. info
• P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
• R. P. Feynman, R. B. Leighton, M. Sands. The Feynman lectures on physics II. Addison Wesley, London, 1964. info
• L. D. Landau, E. M. Lifshitz. Mechanics. Pergamon Press, 1960. info

Language of instruction

English

Further Comments

The course can also be completed outside the examination period.

• Enrolment Statistics (Winter 2012, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2012/MU25008