# David Tong: Lectures on Classical Dynamics

This is a second course in classical mechanics, given to final year undergraduates. They were last updated in January 2015. Individual chapters and problem sheets are available below. The full set of lecture notes, weighing in at around 130 pages, can be downloaded here:

PostScript PDF

A more basic course on classical dynamics, covering Newtonian mechanics
and special relativity,
can
be found here.

# Content

**1. Newtonian Mechanics: PDF**

Table of Contents; Introduction; Newtonian mechanics for a single particle and many particles**2. The Lagrangian Formulation: PDF**

The principle of least action; Changing coordinate systems; Constraints and generalised coordinates; Noether's theorem and symmetries; Applications; Small oscillations and stability**3. The Motion of Rigid Bodies: PDF**

Kinematics; The inertia tensor; Euler's equation; Free tops; Euler's angles; The heavy symmetric top; The motion of deformable bodies**4. The Hamiltonian Formulation: PDF**

Hamilton's equations; Liouville's theorem; Poincare recurrence theorem; Poisson brackets; Canonical transformations; Action-angle variables; Adiabatic invariants; Hamilton-Jacobi theory; Relationship to quantum mechanics

# Problem Sheets

**Problem Sheet 1: Postscript PDF**Lagrangian Formulation**Problem Sheet 2: Postscript PDF**Normal Modes, Inertia Tensors and Rotations**Problem Sheet 3: Postscript PDF**Euler's Equations and Euler Angles**Problem Sheet 4: Postscript PDF**Hamiltonian Formulation