After successful completion of the course, students are able to derive Hamiltonian equations of motion and to apply analytical methods (Normal Forms, generating functions) to simplify the equations and determine special solutions.
Solution methods for Hamiltonian Systems are introduced and demonstrated for selected examples. 1.) Motivation: Mechanical systems, Maximum principle in optimal control; 2.) Inntroduction: Simple modells; 3.) Linear Equations, Symplectic transformations; 4.) Hamiltonian systems with symmetry, conservation laws, Energy-momentum map. 5.) Birkhoff's Normal Form, resonances; 6.) Perturbation Theory, Averaging method; 7.) Numerical integration.
Discussion and treatment of model examples.
Anwendungen in Mechanik und Op.Research
Treatment of a model example.
Anmeldung in TISS
Ordinary differential equations, Mechanics (Hamiltonian and Lagrangian equations), Optimal control.
