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A Global Analysis of The Generalized Sitnikov Problem

Published online by Cambridge University Press:  12 April 2016

Steven R. Chesley
Steven R. Chesley*
Affiliation:
Dipartimento di Matematica, Universitá di Pisa, 56127 Pisa, Italy; E-mail: chesley@dm.unipi.it

Abstract

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The isosceles three-body problem with Sitnikov-type symmetry has been reduced to a two-dimensional area-preserving Poincaré map depending on two parameters: the mass ratio, and the total angular momentum. The entire parameter space is explored, contrasting new results with ones obtained previously in the planar (zero angular momentum) case. The region of allowable motion is divided into subregions according to a symbolic dynamics representation. This enables a geometric description of the system based on the intersection of the images of the subregions with the preimages. The paper also describes the regions of allowable motion and bounded motion, and discusses the stability of the dominant periodic orbit.

Information

Type
Analytical and Numerical Tools
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999, pp. 291 - 302
Copyright
Copyright © Kluwer 1999

References

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