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).

Teacher(s)

prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (seminar tutor)

Guaranteed by

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

Prerequisites (in Czech)

TYP_STUDIA(N)

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

Study Materials
The course can also be completed outside the examination period.

• Enrolment Statistics (recent)
  
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