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The Mechanism of Branching of Three-Dimensional Periodic Orbits from the Plane

Published online by Cambridge University Press:  12 April 2016

I.A. Robin  and
V.V. Markellos
I.A. Robin
Affiliation:
University of Glasgow, Glasgow, Scotland
V.V. Markellos
Affiliation:
University of Patras, Patras, Greece

Abstract

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A linearised treatment is presented of vertical bifurcations of symmetric periodic orbits(bifurcations of plane with three-dimensional orbits) in the circular restricted problem. Recent work on bifurcations from vertical-critical orbits (av = ±1) is extended to deal with the v more general situation of bifurcations from vertical self-resonant orbits (av = cos(2Πn/m) for integer m,n) and it is shown that in this more general case bifurcating families of three-dimensional orbits always occur in pairs, the orbital symmetry properties being governed by the evenness or oddness of the integer m. The applicability of the theory to the elliptic restricted problem is discussed.

Type
Part IV - Periodic Orbits
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 213 - 224
Copyright
Copyright © Reidel 1983

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