The Hamiltonian

Classical Mechanics (Fall, 2011)

Lecture Playlist

  1. State diagrams and the nature of physical laws

  2. Newton's law, phase space, momentum and energy

  3. Lagrangian, least action, Euler-Lagrange equations

  4. Symmetry and conservation laws

  5. The Hamiltonian

  6. Hamilton's equations

  7. Liouville s theorem

  8. Poisson brackets

  9. Electric and magnetic fields 1

  10. Electric and magnetic fields 2

October 24, 2011

This lecture starts with a thorough review of symmetries and conservation laws. Energy conservation is shown to be a consequence of time translation symmetry and the Hamiltonian is introduced.

Topics: 
  • Recommended books
  • Superluminal neutrinos in the news
  • Review of symmetries and conservation laws
  • Active vs passive transformations
  • Review of momentum and angular momentum conservation and associated symmetries
  • Energy conservation as a consequence of time translation symmetry
  • Hamiltonian and energy conservation
References