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Construction of Periodic Orbits, Problems of Stability and Period Determination, in the Elliptical Non-Planar Restricted Problem

Published online by Cambridge University Press:  12 April 2016

Colette Edelman
Colette Edelman*
Affiliation:
Bureau des Longitudes, Paris, France

Abstract

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Periodic orbits in a fixed frame are constructed in the vicinity of nonperiodic solutions of the non perturbed problem. In a first phase, approximate initial conditions are found and in a second phase more accurate initial conditions obtained are used in order to check the periodic orbit by numerical integration of the three-body problem. Some peculiar solutions are found, for example, orbit with nearly zero angular momentum. A study of stability of periodic solutions is proposed with an approximation of the monodromy matrix Φ (T,o),not requiring numerical integration of the 6x6 variational linear system. Finally, some numerical problems of period determination are outlined.

Type
Part IV - Periodic Orbits
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 257 - 261
Copyright
Copyright © Reidel 1983

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