Poisson brackets

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

November 14, 2011

Poisson brackets are another formal formulation of classical mechanics. They help make the connection between symmetries and conservation laws more explicit. The Poisson bracket of the x,y,z components of angular momentum are derived.

Topics: 
  • Poisson brackets and angular momentum
  • Review of Poisson brackets
  • The algebra of Poisson brackets
  • Angular momentum conservation, rotation symmetry and Poisson brackets as tools to compute the generators of rotation
  • Momentum conservation, translation symmetry and Poisson brackets as tools to compute the generators of translation
  • Energy conservation, time shift symmetry and Poisson bracket as a tool to compute the time shift generator
  • General relation between symmetry and conservation law expressed with Poisson bracket.
  • Poisson brackets of the x, y, z components of angular momentum.
  • The gyroscope equations of motion as an example of the power of Poisson brackets
References