Euler-Lagrange equations, 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

October 29, 2007

Define the Euler-Lagrange equations as a result of the Principle of Least Action. Define the canonical momentum. Differential conservation laws result from a continuous symmetry.

Topics: 
  • Euler-Lagrange equations
  • Canonical momentum
  • Generalized coordinates
  • Momentum conservation
  • Relative coordinates
  • Symmetry and conservation laws
  • Rotational symmetry
  • Noether charge
  • Time invariance
  • The Hamiltonian
References