Deprit, A.
, Deprit, E.
and Palacián, J.
(2001),
The Relegation Algorithm, Celestial Mechanics & Dynamical Astronomy
(Accessed October 14, 2025)
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The Relegation Algorithm
Published
Author(s)
, E Deprit, Jesúus Palacián
Abstract
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
Volume
79
Issue
3
Pub Type
Journals
Keywords
Hamiltonian dynamics, Lie transformations, PACS: 02.30.Mv, 03.20.+i, 11.10.Lm, perturbation methods
Citation
Issues
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Created March 3, 2001, Updated February 19, 2017