Classical Mechanics III

Lecture Notes

The full course notes (PDF - 6.1MB) are also available for download.

CHAPTER #	TITLES	TOPICS
1	A Review of Analytical Mechanics (PDF)	Lagrangian & Hamiltonian Mechanics Symmetry and Conservation Laws Constraints and Friction Forces Calculus of Variations & Lagrange Multipliers
2	Rigid Body Dynamics (PDF)	Coordinates of a Rigid Body Time Evolution with Rotating Coordinates Kinetic Energy, Angular Momentum, and the Moment of Inertia Tensor for Rigid Bodies Euler Equations Symmetric Top with One Point Fixed
3	Vibrations & Oscillations (PDF)	Simultaneous Diagonalization of T and V Vibrations and Oscillations with Normal Coordinates
4	Canonical Transformations, Hamilton-Jacobi Equations, and Action-Angle Variables (PDF)	Generating Functions for Canonical Transformations Poisson Brackets and the Symplectic Condition Equations of Motion & Conservation Theorems Hamilton-Jacobi Equation Kepler Problem Action-Angle Variables
5	Perturbation Theory (PDF)	Time Dependent Perturbation Theory for the Hamilton-Jacobi Equations Periodic and Secular Perturbations to Finite Angle Pendulum Perihelion Precession from Perturbing a Kepler Orbit
6	Fluid Mechanics (PDF)	Transitioning from Discrete Particles to the Continuum Fluid Equations of Motion: Continuity Equations, Ideal Fluid: Euler’s Equation and Entropy Conservation, Conservation of Momentum and Energy Static Fluids & Steady Flows Potential Flow Sound Waves Viscous Fluid Equations Viscous Flows in Pipes and Reynolds Number Viscous Flow Past a Sphere (Stokes Flow)
7	Chaos and Non-Linear Dynamics (PDF - 4.8MB)	Introduction to Chaos: Evolution of the System by First Order Differential Equations, Evolution of Phase Space, Fixed Points, Picturing Trajectories in Phase Space Bifurcations: Saddle-Node Bifurcation, Transcritical Bifurcation, Supercritical Pitchfork Bifurcation, Subcritical pitchfork bifurcation Fixed Points in Two-Dimensional Systems: Motion Near a Fixed Point, Systems with a conserved E(x) Limit Cycles and Bifurcations: Poincare-Bendixson Theorem, Fixed Point Bifurcations Revisited and Hopf Bifurcations Chaos in Maps Chaos in Differential Equations, Strange Attractors, and Fractals: The Lorenz Equations, Fractals and the Connection to Lyapunov Exponents, Chaos in Fluids