Advanced mechanics
Graduate · Physics
Syllabus focus
Topics typically covered
Theoretical / proof-based
Calculus of variations
- Functionals, Euler–Lagrange, and natural boundary conditions
- Constraints: Lagrange multipliers and holonomic systems
- Hamilton's principle and symplectic structure
- Noether's theorem and conserved charges
- Hamilton–Jacobi theory and action–angle variables
Rigid body and continuum
- SO(3) kinematics: Euler angles, quaternions, and tensors
- Inertia tensor and principal axes
- Euler's equations for rigid rotors
- Coupled rigid-body problems and tops
- Introduction to elasticity and stress tensors
Nonlinear dynamics
- Phase space, fixed points, and linear stability
- Poincaré sections and bifurcations
- KAM theorem and integrable perturbations (overview)
- Chaos in driven oscillators and maps
- Canonical perturbation theory
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Calculus of variations
Functionals, Euler–Lagrange, and natural boundary conditions
Coming soon - Rigid body and continuum
SO(3) kinematics: Euler angles, quaternions, and tensors
Coming soon - Nonlinear dynamics
Phase space, fixed points, and linear stability
Coming soon
Notes
Topics reflect common graduate physics core and elective syllabi at US universities. Sequencing and emphasis vary between one- and two-semester treatments.