MU25008 Geometric Methods in Mechanics

Mathematical Institute in Opava
Winter 2017
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
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
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.
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.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2017, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2017/MU25008