] MP350 derivation list

MP350 Classical Mechanics

List of derivations for exam

The following is a list of derivations which you might be asked to carry out on the exam. I cannot guarantee that the absence of a derivation from this list means it will not feature on an exam question.

  1. The Euler-Lagrange equations from the principle of least action
  2. Hamilton's equations from the modified principle of least action
  3. Conservation of canonical momentum conjugate to a cyclic coordinate
  4. Conservation of the hamiltonian in Lagrange framework
  5. Conservation of the hamiltonian in Hamilton framework
  6. H=T+V if T is quadratic in velocities and V does not depend on velocities
  7. Hamilton's equations from the Euler-Lagrange equations
  8. Poisson equation of motion df/dt = {H,f} + ∂f/∂t
  9. Poisson bracket relations, eg. {fg,h} = f{g,h} + g{f,h}
  10. Poisson theorem (using Jacobi identity)
  11. Two-body to 1-body reduction, reduced mass
  12. Kepler 2
  13. Kepler 3 given formulae for a, b, e
  14. Orthogonality of rotation matrices
  15. Rotational kinetic energy, inertia tensor
  16. Angular momentum and the inertia tensor
  17. Rotation of inertia tensor