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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

References

Edelman, C. 1982, Astron. Astrophys. 1ll, 220 Google Scholar
Hennawi, A. 1980, Celes. Mech. 22, 237 Google Scholar
Markellos, V.V. 1980, Celes. Mech. 21, 291 Google Scholar
Poincaré, H. 1892, 1893, 1899, Les Méthodes Nouvelles de la Mécanique Céleste, Dover Pub. Inc. (1957)Google Scholar
Rocher, P. 1981, Ephémérides des satellites faibles de Jupiter et de Saturne pour 1981 – 1982 – 1983. Supplément de la Connaissance des Temps pour 1982, Bureau des LongitudesGoogle Scholar
Roseau, M. 1966, Vibrations non linéaires et théorie de la stabilité, Springer, Berlin Google Scholar
Stellmacher, I. 1976, Astron. Astrophys. 51, 117 Google Scholar
Stellmacher, I. 1977, Astron. Astrophys. 59, 337 Google Scholar
Stellmacher, I. 1979, Astron. Astrophys. 80, 301 Google Scholar
Stellmacher, I. 1981, Celes. Mech. 23, 145 Google Scholar
Subbotin, M.F. 1968, Vvedenic v teoreticeskuju astronomiju, Moskva Google Scholar
Szebehely, V. 1967, Theory of Orbits, Academic Press Google Scholar
Wiesel, W. 1980, Celes. Mech. 21, 265 CrossRefGoogle Scholar