Handbook 1996 : Faculty of Science (Volume 4 page 230)
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Credit points: 12.0
Coordinator: Associate Professor J W G Wignall
Prerequisite: Physics 640-221 or 640-241; Mathematics 618-232
Contact: 26 lectures (two a week) and 13 x 1-hour tutorials
Timetable: Second semester
Objectives:
By the end of this course the student should:
- have a detailed comprehension of the canonical Lagrangian/Hamiltonian formulation of classical mechanics;
- be able to apply it to the analysis of simple systems;
- appreciate the new features that arise in non-linear systems, ranging from the ordered behaviour represented by "solitons" to the chaotic behaviour displayed by many non-linear classical systems.
Content:
Review of Newtonian mechanics for a system of particles, special relativistic mechanics, non-inertial frames. Review of Lagrangian formulation, and its expression in terms of variational principles; applications to include the general motion of a rigid body. Review of Hamiltonian formulation; Poisson brackets, phase space and Liouville's theorem, Poincaré mapping. Canonical transformations: formulation, generators of infinitesimal transformations, Noether's theorem, the Hamilton-Jacobi method, action and angle variables. Integrable nonlinear systems: pendulum, 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; overview of occurrence of deterministic chaos in various areas of physics; criteria for chaotic motion: KAM theorem, Lyapunov exponents. Mechanics of continuous systems: integrable systems, solitons; non-integrable systems, fluid turbulence.
Assessment:
A 2 1/2-hour end-of-semester written examination.
Prescribed texts:
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Handbook 1996 : Faculty of Science (Volume 4 page 230)
Status: Official 1996 Date created: Oct 9 1995 Last modified: Oct 9 1995 Authorised by: Academic Registrar Email enquiries: Course_Information@registrar.unimelb.edu.au
Maintained by: School of Physics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.