The core formalisms, concepts, and techniques of classical mechanics are essential components of a graduate education in physics. The subject forms the basis for a thorough understanding of quantum mechanics and statistical mechanics, as well as the foundation for modern pure and applied research on nonlinear mechanical systems.
Newtonian and Lagrangian methods are reviewed and applied extensively to translational and rotational motion of rigid bodies, the central force problem, and small oscillations of mechanical systems with several degrees of freedom. Students should learn to set up the Lagrangian for reasonably complicated systems, analyze the relevant symmetries, reduce the dimensionality of the system where appropriate, obtain the equations of motion, and solve them in certain cases. The Hamiltonian formulation is also presented. Students should develop some facility with the concepts of canonical transformations, phase flow, Poisson brackets, integrable systems and chaos. Students should develop an appreciation for the consistency of the various formulations and their interconnections.
The course provides exposure to the following topics:
This course also serves to introduce first-year graduate students to the level of mathematical rigor required for PhD level research. Students are presented with difficult problems and required to work through them carefully and thoroughly. Relevant skills that should be developed include performing difficult calculations, examining solutions for physical coherence, and obtaining consistent solutions using different approaches.
(There are two lectures per week.)