MIDIT OFD CATS Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and Technical University of Denmark Building 128 Department of Chemistry Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark
by M. Deriabine, Ph.D
MAT, Building 303
Technical University of Denmark
Wednesday, November 14, 21 and 28 at 14:00
at IMM, Bldg. 305, Room 018, DTU
Lecture 1. FOUNDATIONS OF CLASSICAL MECHANICS:
We start with reviewing the basic principles of Lagrangean and Hamiltonian mechanics, focusing mainly on geometrical and topological aspects. We discuss Poincare recurrence theorem, Huygens variational principle and the interconnection between mechanics and geometrical optics, simplectic structure, and some other topics.
Lecture 2. INTEGRABILITY AND NON-INTEGRABILITY IN HAMILTONIAN MECHANICS:
We begin with Arnol'd-Liouville thoerem on integrable systems and some classical results on existence of first integrals of motion. We give some new criteria for nonexistence of analytic first integrals, based on topological structure of the system configuration space. We then proceed to the theory of perturbations, introduction of KAM theory and the structure of near-integrable Hamiltonian systems.
Lecture 3. CONSTRAINED MOTION:
We discuss various aspects of mechanical systems with constraints and realisation of constraints. We give an introduction to Vakonomic mechanics and Dirac hamiltonian formalism with constraints. We show the connection of these problems to the classical optimisation and control problems.