Symmetry and conservation laws

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 17, 2011

This lecture focuses on the relation between continuous symmetries of the Lagrangian and conserved quantities. Generalized coordinates and canonical conjugate momentum are introduced.

Topics: 
  • Symmetry and conservation laws: they are always related
  • Review of the principle of least action (stationary action)
  • Generalized coordinates and their canonical conjugate momentum
  • Conserved quantities and translation and rotation symmetry
  • Noether theorem concept and outline
  • Momentum conservation as a consequence of translation symmetry
  • Angular momentum conservation as a consequence of rotational symmetry
  • The harmonic oscillator
  • Discrete symmetries have no associated conserved quantities in classical mechanics
References