THE MAGNUS EXPANSION FOR CLASSICAL HAMILTONIAN-SYSTEMS

Lie operator techniques and the Magnus expansion are developed in the framework of classical mechanics. This leads to an exponential perturbation theory that preserves the canonical character at each order of approximation. The treatment is kept as close as possible to the quantum mechanical case in order to take full advantage of the properties of the expansion. The explicit relationship with secular perturbation theory is established and a recursive procedure for obtaining higher-order approximants is provided. Finally, the formalism is applied to two problems of physical interest.