PHY401A - Classical Mechanics

Review of Newtonian mechanics: Basic assumption; constraints, principle of virtual work, D'Alembert's principle, generalized coordinates. Lagrangian mechanics: Calculus of variations, Principle of least action, Lagrange's equation, Symmetries and Noether's theorem. Hamilton's equations, phase space &. phase trajectories, LiuviuUe's theorem. Small oscillations, normal modes, an harmonic and nonlinear oscillators, Nonlinear dynamics. Chaos (Hamiltonian systems in dissipative systems).IUu'strations using Duffing oscillator, double pendulum, three body problem, etc. Continuum mechanics, Waves in continuous media, Navier Stokes Eqn., Pressure waves [3]canonical transformations, Poisson brackets, Hamilton Jacobe theory, Action angle variables (recommend: central force discussed here). rigid body dynamics.