MATH 240 Analytical Mechanics

The equations of motion. Generalized coordinates. The principle of least action. Relativity principle. The Lagrangian for a free particle. Conservation laws. Energy. Momentum. Centre of mass. Angular momentum. Integration of the equations of motion. Motion in one dimension. The reduced mass. Motion in a central field. Small oscillations. Free oscillations in one dimension. Forced oscillations. Damped oscillations. Motion of a rigid body. Angular velocity. The inertia tensor. Angular momentum of a rigid body. Eulerian angles. Euler’s equations. The canonical equations. Hamilton’s equations. The Routhian. Poisson brackets. The action. Canonical transformations. Liouville’s theorem. The Hamilton- Jacobi equation.