Solve problems using the calculus of variations, including constraints. Solve problems using Lagrangian dynamics and generalized coordinates, including conserved quantities and forces of constraint.

Solve central force problems, including 2-body gravitation and perturbations to circular motion, problems involving coupled oscillators, and analyze for normal modes.

Solve problems in special relativity using its 4-vector formulation.

Solve dynamics problems using the Hamiltonian and canonical transformations. Also solve dynamics problems using Hamilton-Jacobi theory and action-angle variables, including adiabatic invariants and perturbation theory.