On the numerical transformation of variables in perturbation theory |
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Authors: | Sławomir Breiter |
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Institution: | (1) Astronomical Observatory of the A. Mickiewicz University, S oneczna 36, PL 60-286 Pozna , Poland |
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Abstract: | Once the generating function of a Lie-type transformation is known, canonical variables can be transformed numerically by application of a Runge-Kutta type integration method or any other appropriate numerical integration algorithm. The proposed approach avails itself of the fact, that the transformation is defined by a system of differential equations with a small parameter as the independent variable. The integration of such systems arising in the perturbation theories of Hori and Deprit is discussed. The method allows to compute numerical values of periodic perturbations without deriving explicitly the perturbation series. This saving of an algebraic work is achieved at the expense of multiple evaluations of the generator's derivatives. |
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Keywords: | Lie series numerical integration perturbation theory |
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