High-order Analytical Solutions of Hill’s Equations |
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| Authors: | G Gómez M Marcote |
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| Institution: | (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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