Hamiltonian Mechanics

The following sections are included:

• Canonical Hamilton's Equations

• Legendre Transformation^*

• Hamiltonian Optics and Wave-Particle Duality^*

• Motion in an Electromagnetic Field

  • Euler-Lagrange Equations

  • Energy Conservation Law

  • Gauge Invariance

  • Canonical Hamilton's Equations

  • Maupertuis' Principle of Least Action

• One-degree-of-freedom Hamiltonian Dynamics

  • Energy Method

  • Simple Harmonic Oscillator

  • Pendulum

    • Libration Class (E < 2mgl)

    • Separatrix Class (E = 2mgl)

    • Rotation Class (E > 2mgl)

  • Constrained Motion on the Surface of a Cone

• Problems