Symmetry and conservation Laws

Classical Mechanics (Fall, 2007)

Lecture Playlist

  1. State diagrams and the nature of physical laws

  2. Newton's laws, principle of least action

  3. Euler-Lagrange equations, symmetry and conservation laws

  4. Symmetry and conservation Laws

  5. Lagrangians and Hamiltonians

  6. Hamilton's equations

  7. Liouville’s theorem

  8. Motion in an electromagnetic field

  9. Poisson brackets formulation

November 5, 2007

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

Topics: 
  • Euler-Lagrange equations
  • Canonical momentum
  • conservation laws
  • Action integral
  • Lagrangian
  • Emily Noether current
  • Symmetry and conservation laws
  • Conservation of momentum and translational symmetry
  • Conservation of angular momentum and rotational symmetry
References