Syllabus

This course focusses on high level mechanics, and will continue directly from the material in Classical Mechanics I. Our journey will take us away form the Newtonian formulation of mechanics to the analytical framework of Lagrange and Hamilton, allowing us to tackle more complex and physically realistic problems that would be otherwise be near-impossible to solve. We will spend some time deriving these new approaches, using the technique of calculus of variations. The course will finish on the topic of true theoretical mechanics (e.g. Hamilton-Jacobi theory) which naturally leads into quantum and particle physics.

Details

This class would to take place once a week over a semester. We followed the textbook Classical Mechanics by Taylor. The material was the subject of seminars held immediately after each lecture.

Class slides

PDFs of lecture slides can be found in the CM2 folder at this url. Note these slides were used in classes I taught 2021 and have not been updated since.

Part 1 [2 sessions]: Calculus of variations

Part 2 [3 sessions]: The Lagrangian and Euler-Lagrange equations

Part 3 [2 sessions]: Conserved quantities, equilibria and constraints, Lagrangian multipliers

Part 4 [2 sessions]: Classical problems with the Lagrangian

Part 5 [2 sessions]: Coupled oscillations

Part 6 [3 sessions]: Hamiltonian mechanics

Part 7 [1 session]: Theoretical mechanics