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