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Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

Published online by Cambridge University Press:  12 April 2016

C.G. Zagouras  and
V.V. Markellos
C.G. Zagouras
Affiliation:
University of Patras, Patras, Greece
V.V. Markellos
Affiliation:
University of Patras, Patras, Greece

Abstract

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In the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

Type
Part IV - Periodic Orbits
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 235 - 247
Copyright
Copyright © Reidel 1983

References

Buck, T.: 1920, in Moulton, F.R., Periodic Orbits, Carnegie Inst, of Washington, J. Reprint Co., p. 299 Google Scholar
Markellos, V.V.: 1977, Monthly Notices Roy. Astron. Soc. 180, 103 Google Scholar