High-order Analytical Solutions of Hill's Equations

Details High-order Analytical Solutions of Hill's Equations High-order Analytical Solutions of Hill's Equations

Feb 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..94..197g&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 94, Issue 2, pp.197-211

Astronomy and Astrophysics

Astronomy

4

Hill&Rsquo, S Equations, Lindstedt&Ndash, Poincar&Eacute, Series

Scientific paper

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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