Basics of Hamiltonian Mechanics

Abstract

In this chapter we shall briefly recall the fundamental principles and methods of Hamiltonian mechanics which will be used throughout the book. This is for convenience of the reader and to fix notation. For more details, the reader might consult Arnold (1989). In particular, we shall give different formulations of Hamiltonian equations, and recall the invariants of motion. Special emphasis will be given to the Hamilton–Jacobi method and the action-angle formalism to integrate the equations of motion. These methods will be illustrated with the example of the pendulum. Finally, we shall shortly discuss modern methods of numerical symplectic integration of Hamiltonian systems.