Classical mechanics
Undergraduate · Physics
Syllabus focus
Topics typically covered
Standard syllabus
Newtonian mechanics advanced
- Constraints and generalized coordinates
- Central force problems and effective potential
- Orbits: Kepler laws and scattering
- Rigid body dynamics and Euler equations
- Non-inertial frames and fictitious forces
Lagrangian mechanics
- Principle of least action and Euler–Lagrange equations
- Conserved quantities and Noether's theorem (intro)
- Small oscillations and normal modes
- Hamilton's principle for holonomic systems
- Legendre transform to Hamiltonian mechanics
Hamiltonian mechanics
- Canonical equations and phase space
- Poisson brackets and constants of motion
- Canonical transformations (introduction)
- Integrable systems and action–angle variables (overview)
- Chaos and sensitivity in nonlinear systems (intro)
STEM / applied
Aerospace and robotics
- Satellite attitude and gyroscopic stabilization
- Lagrangian models for robotic manipulators
- Rocket trajectory and variable mass systems
- Vibration isolation in mechanical design
- Control-theory connections to Hamiltonian flow
Continuum and fluid analogies
- Lagrangian vs Eulerian descriptions preview
- Coriolis effects in geophysical flows
- Coupled oscillators in structural engineering
- Stability analysis of equilibria
- Numerical symplectic integrators for orbits
Experimental and computational ties
- Pendulum arrays and coupled modes in lab
- Tracking orbits with numerical ODE solvers
- Comparing analytic and simulated scattering
- Energy landscapes in molecular mechanics context
- Parameter estimation from motion capture data
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Newtonian mechanics advanced
Constraints, central forces, rigid bodies, and non-inertial frames
Coming soon - Lagrangian mechanics
Action principles, Euler–Lagrange equations, and small oscillations
Coming soon - Hamiltonian mechanics
Phase space, canonical equations, and integrability
Coming soon
Notes
Topics reflect common upper-division physics syllabi at US colleges and universities. Prerequisites, lab pairing, and mathematical depth vary by department.