With the conclusion of this course, the students will know how to apply and analyse a problem in mechanics. They will also aquire a general knowledge of some physical theories (e.g., the principle of least action).
Course Content (Syllabus)
Definition of Hamiltonian Mechanics(Hamilton’s equation, symplectic formalism, Poisson’s theorem). Canonical transformations (generating function, symplectic matrices). Infinitesimal canonical transformations (Hamiltonian vector field, infinitesimal symmetries and integrals of motion). Stability of equilibrium points Liouville’s theorem, Poincare’s theorem. The method of Hamilton-Jacobi, Integrable systems, Lax pairs. Action-angle variables, canonical theory of perturbation, small divisors, K.A.M. theorem. Poincare map, Poincare-Birkhoff theorem, chaotic motion in Hamiltonian systems.
Course Bibliography (Eudoxus)
- ΚΛΑΣΙΚΗ ΜΗΧΑΝΙΚΗ, Σ.Ν. ΠΝΕΥΜΑΤΙΚΟΣ, ΠΝΕΥΜΑΤΙΚΟΣ
- ΕΙΣΑΓΩΓΗ ΣΤΗ ΜΗΧΑΝΙΚΗ HAMILTON, ΣΙΜΟΣ ΙΧΤΙΑΡΟΓΛΟΥ, 2015, εκδόσεις iwrite