Given a perturbed Hamiltonian system, normalization yields a Lie transformation which converts the main part of the Hamiltonian into an integral of the transformed system. An extension of the normalization method--the relegation algorithm--does the same for an arbitrary function G of the state variables; if the Lie derivative defined by G is semi-simple, a double recursion produces the generator of the relegating Lie transformation. Simple examples demonstrate how relegation works on the boundary of a parameter domain where normalization fails, and results are presented in detail so they may serve as benchmarks for computer codes implementing the relegation algorithm.
Citation: Celestial Mechanics & Dynamical Astronomy
Pub Type: Journals
Hamiltonian dynamics, Lie transformations, PACS: 02.30.Mv, 03.20.+i, 11.10.Lm, perturbation methods