640-355 Classical and Modern Mechanics

Credit Points

Coordinator

Prerequisites

Physics 640-224 or 640-244; Mathematics 620-232.

(For subjects completed prior to 1998, the Mathematics and Statistics departmental code 620- should be replaced by the superseded Mathematics departmental code 618-)

Semester

Contact

Subject Description

Mechanics is the oldest and the most widely applied science. Modern approaches to Newtonian mechanics and special relativity have demonstrated great power and beauty and will be detailed. This subject will illustrate the power of modern mechanics in understanding the physical universe. The canonical Lagrangian/Hamiltonian formulation of classical mechanics will be reviewed. Non-linear systems including 'soliton' physics and chaotic behaviour will be discussed.

Topics will be selected from: the Lagrangian formulation, the variational principle; motion of rigid bodies; the Hamiltonian formulation; Poisson brackets, phase space and Liouville's theorem, Poincaré mapping. Canonical transformations, Noether's theorem, the Hamilton-Jacobi method. Integrable nonlinear systems: 2-body Kepler problem, free nonlinear oscillators, limit cycles, separable systems. Non-integrable nonlinear systems: Approximation methods: perturbation theory, adiabatic invariants; chaotic motion in Hamiltonian systems: coupled and driven nonlinear oscillators, the 3-body central force problem; chaotic motion in dissipative systems: the logistic map, Lorenz system, strange attractors; KAM theorem, Lyapunov exponents; mechanics of continuous systems.

Assessment

A 1.5 hour end-of-semester written examination plus tests and/or assignments, set during the semester, which may account for up to 20% of the final mark.

Prescribed Texts

• Goldstein H, Classical Mechanics. 2nd ed. 1980 Addison-Wesley.