Motion in an electromagnetic field

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

December 17, 2007
Recapitulate symmetries and conservation laws.
According to Liouville's theorem, a system evolving according to Hamilton's equations conserves the volume of phase space. Information is conserved.
The Principle of Least Action underlies Lagrangian and Hamiltonian methods.
Investigate motion in an electromagnetic field.
Demonstrate gauge invariance.
Link time invariance and energy conservation.
Define the axiomatic structure of Poisson brackets.
Topics: 
  • Least Action
  • Lorentz force equation
  • Electromagnetic equation of motion
  • Vector potential
  • Symmetries and conservation laws
  • Poisson brackets
References