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

GEOMETRICAL METHODS IN CLASSICAL MECHANICS

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.