PHYS 3300 - Classical Mechanics

Index to lecture notes

PHYS 3300 notes will appear here as the course is being taught.

Lectures 1-3(pdf): Course outline, supplemental information. Recap of line integrals. Concept of functional, finding extrema. Shortest path problem and calculus of variations. Euler-Lagrange equation(s). Special cases and examples. Typo note: result at top of page 5 should be 2, not 1.

Lectures 3-4(pdf): (Overlaps above file). Constraints and generalized coordinates. Holonomic and non-holonomic constraints. Examples.

Lectures 5-6(pdf): Principle of Virtual Work and D'Alembert's Principle. Derivation of the Lagrangian. Examples of Lagrangians: Harmonic oscillator, pendulum in polar coordinates, double pendulum

Lectures 7-8(pdf): Hamilton's Principle, action integral. Lagrange Multipliers for constrained systems. Conservation theorems, definition of generalized momenta, cyclic coordinates. Example - motion in a central potential

Lectures 9-10(pdf): Rigid body kinematics, degrees of freedom in configurations, orthogonal transformations & their properties, passive vs active coordinate changes

Lectures 11-12(pdf): Euler angles. Inertia tensor, definition and introduction to tensors. Diagonalization of the inertia tensor and principal moments.

Lectures 13-15(pdf): Derivation of Euler's equations and dynamics in rotating reference frames. Lagrangian for a spinning top. Conserved momenta and their use in predicting the behaviour of the top. Precession and nutation of the top. Use of the cubic in theta to determine possible behaviours. 'Fast top' definition and treatment of nutation as a perturbation.

Lectures 16-17 (skipped for now) (pdf): Special Relavtivity formulated using Minkowski spacetime. 4-vector formalism, Lorentz Transformations via Lorentz boosts. Lorentz invariant formulation of equations of motion, approaches to relativistic lagrangians.

Lectures 18-19(pdf): (fixes missing page 119 from previous pdf) Introduction to Hamiltonian mechanics, Hamilton's equations of motion. Legendre transformations, definition of Hamiltonian, SHM example. Conservation of energy plus canonical momenta in the Hamiltonian picture. Variational principle and Poisson bracket definition.

Lectures 20-21(pdf): Canonical transformations. Non-uniqueness of Lagrangians & Hamiltonians. Definitions of generating functions using Legendre transformations. Example application to SHM. Invariance of Poisson Brackets under canonical transformations.