MATH 572 Mathematical Methods of Classical Mechanics II

Hamiltonian mechanics. Legendre’s transformation. Hamilton’s equations. Hamilton’s function and energy. Cyclic coordinates. Routh’s function. Variational principle. The action as a function of coordinates. Maupertui’s and Fermat’s principles. Poisson brackets. Momentum space. Hamiltonian dynamics in rotating frame. Canonical transformations. Geometrical theory of the phase space. Symplectic structure. Infinitesimal canonical transformations. Conservation theorems and Poisson brackets. Hamilton’s mechanics in arbitrary variables. Hamilton-Jacobi equation. Principal and characteristic functions. Separation of variables. Central force problem. Action-angle variables.