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Lectures Classical mechanics

Lectures "Classical mechanics" has contents: Course summary, calculus of variations, calculus of variations, hamiltonian mechanics, advanced topics. | Classical Mechanics Joseph Conlon April 9, 2014 Abstract These are the current notes for the S7 Classical Mechanics course as of 9th April 2014. They contain the complete text and diagrams of the notes. There will be no more substantive revisions of these notes until Hilary 2014-15 (small typographical revisions may occur inbetween). Contents 1 Course Summary 3 2 Calculus of Variations 5 3 Lagrangian Mechanics 3.1 Lagrange’s Equations . . . . . 3.2 Rotating Frames . . . . . . . 3.3 Normal Modes . . . . . . . . . 3.4 Particle in an Electromagnetic 3.5 Rigid Bodies . . . . . . . . . . 3.6 Noether’s Theorem . . . . . . . . . . . . 10 10 16 22 25 27 30 . . . . . 33 33 35 36 39 42 5 Advanced Topics 5.1 The Hamilton-Jacobi Equation . . . . . . . . . . . . . . . . . . . 5.2 The Path Integral Formulation of Quantum Mechanics . . . . . . 5.3 Integrable systems and Action/Angle Variables . . . . . . . . . . 50 50 55 60 4 Hamiltonian Mechanics 4.1 Hamilton’s Equations . . . 4.2 Hamilton’s Equations from 4.3 Poisson Brackets . . . . . 4.4 Liouville’s Theorem . . . . 4.5 Canonical Transformations . . . . . . . . . . . . Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the Action Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Course Summary This course is the S7 Classical Mechanics short option (for physicists) and also the B7 Classical Mechanics option for those doing Physics and Philosophy. It consists of 16 lectures in total, and aims to cover advanced classical mechanics, and in particular the theoretical aspects of Lagrangian and Hamiltonian mechanics. Approximately, the first 12 lectures cover material that is .