High-order Analytical Solutions of Hill’s Equations |
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Authors: | G. Gómez M. Marcote |
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Affiliation: | (1) Departament Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain |
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Abstract: | The purpose of this paper is the semi-analytical computation of the bounded orbits of Hill’s equations, describing the relative motion of two particles in their Keplerian motion around a central body. We have considered the case in which one of the particles moves along a circular reference orbit. The solutions obtained are the generalisation of the usual periodic orbits obtained for the linearised equations and also of the third-order solution computed by D.L. Richardson and J.W. Mitchell (2003). With the algorithm presented, those orbits can be computed in a fast and efficient way up to a high-order in the in-plane and out-of-plane amplitudes. |
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Keywords: | Hill’ s equations Lindstedt– Poincaré series |
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