Recursive Formulae for the Lie-Integration of Linearized Equations

Pál, András (2006) Recursive Formulae for the Lie-Integration of Linearized Equations. In: 4th Austrian-Hungarian Workshop on Celestial Mechanics Edited by Á. Süli, F. Freistetter, A. Pál. Publications of the Astronomy Department of the Eötvös University (18). ELTE Sokszorosítóüzeme, Budapest, pp. 173-177.

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Abstract

Several methods used in celestial mechanics require to solve ordinary differential equations (ODEs) and also derived equations like linearized ones. Lieintegration is known to be one of the fastest ODE-integrators and it is widely applied in long-term investigations. However, an inconvenience of this method is that auxiliary recurrence relations must be deduced which is different for each problem. We present a lemma which can be used to derive such recurrence relations almost automatically for the linearized equations if the relations for the original ODEs are known. This lemma is then applied to the equations of the classical 2-body problem. The knowledge of such relationsmay imply other chaos detection methods; some concerning (and preliminary) results are also presented.

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