Abstract
The continuation of symmetric periodic orbits can be described in terms of “symmetry functions”; the branching of the zero-level lines in a neighbourhood of a critical point gives rise to the transition from “first kind” to “second kind” periodic orbits. When the families are parametrized with the Jacobi integral, the bifurcations can be described as “catastrophes” of the generating functions. However bifurcations of higher order are more complex than the generic catastrophes with one parameter: both symmetric and asymmetric bifurcations occur.
In this way the symmetric periodic orbits that do not have close approaches to the secondary body can be described in an analytic way and their stability can be deduced from simple bifurcation rules. However numerical experiments are required to determine the “natural termination” of the families.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold,V.:1976,Methodes mathematiques de la mécanique classique, MIR, Moscaow.
Arenstorf,R.F.:1963, Am.J.Math. 85, p.27.
Barrar,R.B.:1965, Astron.J. 70, p.3.
Brjuno,A.D.:1978, Celestial Mechanics 18, p.9.
Colombo,G. et al.:1968, Astron.J. 73, p.111.
Guillame,P.:1969, Astron.Astrophys. 3, p.57.
Hartmann,P.:1964, Ohdinary differential equations, J.Wiley & Sons.
Poincaré,H.:1892, Les méthodes nouvelles de la Mécanique Céleste, vol.I, Gauthier-Villars.
Roy,A.E.,Ovenden,M.W.:1955, Mon.Nat.R.Astron.Soc. 115, p.297.
Siegel,C.L.,Moser,J.K.:1971, Lectures on celestial Mechanics, Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 D. Reidel Publishing Company, Dordrecht, Holland
About this paper
Cite this paper
Milani, A. (1983). Stability and Bifurcations of Symmetric Periodic Orbits in the Restricted 3-Body Problem. In: Markellos, V.V., Kozai, Y. (eds) Dynamical Trapping and Evolution in the Solar System. Astrophysics and Space Science Library, vol 106. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7214-8_26
Download citation
DOI: https://doi.org/10.1007/978-94-009-7214-8_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7216-2
Online ISBN: 978-94-009-7214-8
eBook Packages: Springer Book Archive