Hamilton's equations

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 1, 2011

In this lecture many mechanical practical examples are worked out. Hamilton's equations are introduced: they represent one more way to do classical mechanics. The harmonic oscillator is revisited using Hamilton's equations.

Topics: 
  • Motion of a ball on a wedge as an example of Euler-Lagrange equations
  • The ball on a wedge: Associated symmetries and conservation laws, conjugate momentum
  • Double pendulum example treated in detail. Associated symmetries and conservation
  • Hamiltonian, forbidden laws, reversibility, convergent and divergent paths in state space
  • Hamilton's equations of motion
  • Harmonic oscillator using Hamilton's equations and energy conservation
  • Phase space
References