Hamilton's equations

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 19, 2007
The Hamiltonian function determines the evolution of a system
Closed cycles in phase space represents a conservation law
Hamilton's equations are first order equations of motion. Newton's equations are second order equations of motion.
Canonical momentum appears in Hamilton's equations rather than velocity.
Derive the conditions for energy conservation.
Topics: 
  • Energy conservation
  • Phase space
  • Canonical momentum
  • Poisson bracket
  • Hamilton's equations
References