Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Aim: An advanced course in classical mechanics that lays down the
foundation for further study of modern physics, from quantum mechanics
to statistical mechanics to nonlinear dynamics. Stress will be on the
more modern formalisms, concepts, and techniques of classical
mechanics that find applications in a variety of fields.
- Topics:
- Lagrangian Formulation of Mechanics; Constraints and Configuration
Manifolds; Symmetries and Conservation laws
- Hamiltonian Formulation of Mechanics; Hamilton's Equations of Motion
(Symplectic Approach)
- Canonical Transformations; Action-Angle Variables; Poisson brackets
and Invariants; Integrable Systems
- Canonical Perturbation Theory
- Adiabatic Invariants; Rapidly Varying Perturbations
- KAM theorem; Non-integrability and Chaos in Hamiltonian Systems
- Introduction to Continuum Dynamics and Classical Fields (Sine-Gordon
Equation; Klein-Gordon equation; Solitons)
- Semiclassical Quantization (Einstein-Brillouin-Keller Quantization;
Gutwiller Trace Formula)
- J. V. Jose and E. J. Saletan, Classical Dynamics - A
Contemporary Approach, Cambridge University Press (1998).
- M. Tabor, Chaos And Integrability In Nonlinear Dynamics: An
Introduction, Wiley-Interscience (1989).
