Classical Mechanics

Forces, constraint equations, normal forces, and solving multi-body systems with contact and rope constraints.

Generalized coordinates, the Euler-Lagrange equations, and solving mechanical systems through energy methods.

Phase space, Hamilton's equations, Poisson brackets, and the geometric structure of classical mechanics.

Orbits, effective potential, Kepler's laws, and the general solution to the two-body gravitational problem.

Moment of inertia tensor, Euler's equations, precession, and the motion of symmetric tops.

Normal modes of coupled mechanical systems near equilibrium, linearization, and eigenfrequencies.

Beat phenomena, normal coordinates, weak and strong coupling, and the transition to wave motion.

Transformations that preserve the Hamiltonian structure, generating functions, and action-angle variables.

Noether's theorem, continuous symmetries, conserved charges, and the connection between symmetry and dynamics.

Phase portraits, fixed points, stability, period doubling, strange attractors, and sensitive dependence on initial conditions.

Impact parameter, deflection function, differential cross section, Rutherford scattering, and rainbow scattering.