Theoretical / proof-based
Advanced mechanics · Graduate · Physics
Topics
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
What each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · Advanced mechanics · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.