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

• - 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.

• Enrolment Statistics (Winter 2014, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2014/MU25008