Contents

• Motivational Overview
• Lagrangian and Hamiltonian Formulation of Mechanics.
• Advantage of the Hamiltonian Formulation.
• The Dynamical Phase
• The Hamilton-Jacobi Equation for a Relativistic Particle.
• Solution to the Hamilton-Jacobi Equation
• Dynamical Phase as Physical
• The Principle of Constructive Interference
• Laser-driven Particle Mechanics via Celestial Mechanics
• Phase Flow: Its Trajectories and Transformations
• Action-Angle Representation
  • Multiple Periodicity expressed in Terms of a Torus
  • Action Variables
  
  
• Conclusion