Complete closed-form solutions of the Stark problem |
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Authors: | Gregory Lantoine Ryan P Russell |
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Institution: | 1.School of Aerospace Engineering,Georgia Institute of Technology,Atlanta,USA |
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Abstract: | Perturbed two-body problems play a special role in Celestial Mechanics as they capture the dominant dynamics for a broad range
of natural and artificial satellites. In this paper, we investigate the classic Stark problem, corresponding to motion in
a Newtonian gravitational field subjected to an additional uniform force of constant magnitude and direction. For both the
two-dimensional and three-dimensional cases, the integrals of motion are determined, and the resulting quadratures are analytically
integrated. A complete list of exact, closed-form solutions is deduced in terms of elliptic functions. It is found that all
expressions rely on only seven fundamental solution forms. Particular attention is given to ensure that the expressions are
well-behaved for very small perturbations. A comprehensive study of the phase space is also made using a boundary diagram
to describe the domains of the general types of possible motion. Numerical examples are presented to validate the solutions. |
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