A sliding bead on a rotating hoop in the presence of gravity. This simulation is done by solving the EulerLagrange equations in the first problem set.
Part A: Classical Mechanics
Overview
This course continues the study of dynamics and techniques developed in Calculus of Variations, with a particular focus on the movement of rigid bodies in three dimensions. Some of the key topics include:
Lagrangian equations of motion
Oscillations near equilibrium
Angular momentum of a system of particles about a fixed point and about the centre of mass.
Motions of a rigid body with one fixed point
Angular velocity, moments of inertia, kinetic energy, angular momentum of a rigid body with axial symmetry
Gyroscopes and classical integrable cases of rigid body motion.
Problem sets

Week 7: Quadratic Lagrangians and small oscillations
Week 8: Rotations of a rigid body