MU:MU25008 Geometric Methods in Mechanics - Course Information
MU25008 Geometric Methods in Mechanics
Mathematical Institute in OpavaWinter 2013
- 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
- - Lagrangian and Euler-Lagrange equations. Symmetries and integrals of motion. Emmy Noether theorems.
- Poisson brackets, Poisson and symplectic structures on smooth manifolds, Darboux theorem.
- Hamiltonian, Hamiltonian vector fields, Hamiltonian equations.
- Legendre transform and relationship between Lagrange and Hamilton formalism.
- Integrals of motion, complete integrability and Liouville's theorem.
- Group actions on Poisson manifolds. Moment map.
- Hamilton-Jacobi equations, complete integral, separation of variables, action-angle variables.
- Bihamiltonian systems.
- - Lagrangian and Euler-Lagrange equations. Symmetries and integrals of motion. Emmy Noether theorems.
- 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
- Czech
- Further Comments
- The course can also be completed outside the examination period.
- Enrolment Statistics (Winter 2013, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2013/MU25008