Rotating hoop A sliding bead on a rotating hoop in the presence of gravity. This simulation is done by solving the Euler-Lagrange 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 6: On rods and wires
  • Week 7: Quadratic Lagrangians and small oscillations
  • Week 8: Rotations of a rigid body