" So few went to hear him, and fewer understood him, that oftimes he did, for want of hearers, read to the walls. He usually stayed about half an hour; when he had no auditors he commonly returned in a quarter of that time."
-- Student evaluation of a well known Cambridge lecturer in classical mechanics, circa 1690
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:
An expanded version of these notes has appeared as a textbook.
Content
- 1. Newtonian Mechanics:
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Table of Contents; Introduction; Newtonian mechanics for a single particle and many particles - 2. The Lagrangian Formulation:
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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:
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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:
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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