- To gain understanding of basic concepts of modern theory of Hamitonian mechanics and symplectic geometry and skills in solving particular problems central for various applications. Additional attention will be paid to the theory of integrable systems.
- To know how to solve equations of motion of basic system, to understand a concept of symplectic geometry, canonical transformations
- To appreciate a concept of Lax representation as a foundation of the theory of integrable systems
- Lagrangian formalismLagrangian formalism: Least action principle; Euler – Lagrange equations; first integrals and symmetries of action.
- Basics of Hamiltonian formalismBasics of Hamiltonian formalism: phase space; Legendre transform; Poisson brackets and symplectic structure; Darboux theorem, Hamiltonian equations.
- Examples: Geodesics on Lie groups. Mechanics of solid body and hydrodynamics of ideal fluid.
- Separations of variables and integrabilitySeparations of variables and integrability: Hamitonian – Jacobi equations; canonical transformations. Moment map. Arnold -– Liouville integrable systems. Lax representation.
- Cortés, V., & Haupt, A. S. (2016). Lecture Notes on Mathematical Methods of Classical Physics. https://doi.org/10.1007/978-3-319-56463-0
- Landau, L. D., & Lifshitz, E. M. (2013). Course of Theoretical Physics (Vol. 3d edition). Saint Louis: Pergamon. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1443758
- Jovanovic, B. (2016). Noether symmetries and integrability in time-dependent Hamiltonian mechanics. https://doi.org/10.2298/TAM160121009J