Lagrangians and Hamiltonians

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 12, 2007

Example simple pendulum:  derive the Euler-Lagrange equations, the kinetic energy, potential energy, Lagrangian and angular momentum. Calculate the Hamiltonian. Review the trajectory of the simple pendulum in phase space. Derive conservation of area in phase space.

Topics: 
  • Simple pendulum
  • Hamiltonian
  • Kinetic and potential energy
  • Double pendulum
  • Hamiltonian formulation
  • Phase space
  • Area in phase space is conserved
  • Lagrangian mechanics
References