Book ChapterDOI
The Trojan Manifold — Survey and Conjectures
André Deprit,Jacques Henrard +1 more
- pp 1-18
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In this paper, the families of periodic orbits emanating from the triangular equilibrium L 4 are interpreted in an attempt to establish the evolution of these manifolds as the mass ratio varies from Routh's critical value down to its value in the system sun-jupiter.Abstract:
Recent results concerning the families of periodic orbits emanating from the triangular equilibrium L 4 are interpreted in an attempt to establish the evolution of these manifolds as the mass ratio varies from Routh’s critical value down to its value in the system sun-jupiter.read more
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Journal ArticleDOI
Elemental periodic orbits associated with the libration points in the circular restricted 3-body problem
Eusebius J. Doedel,Volodymyr A. Romanov,Randy Paffenroth,Herbert B. Keller,Donald Dichmann,Jorge Galán-Vioque,André Vanderbauwhede +6 more
TL;DR: An overview of detailed computational results for families of periodic orbits that emanate from the five libration points in the Circular Restricted 3-Body Problem is presented, as well as for various secondary bifurcating families.
Journal ArticleDOI
Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem
Eusebius J. Doedel,Randy Paffenroth,Herbert B. Keller,Donald Dichmann,Jorge Galán-Vioque,André Vanderbauwhede +5 more
TL;DR: It is shown how to compute families of periodic solutions of conservative systems with two-point boundary value problem continuation software and how the invariances (phase-shift, scaling law, and x, y, z translations and rotations) can be dealt with.
Journal ArticleDOI
Periodic solutions near a resonant equilibrium of a Hamiltonian system
TL;DR: In this article, the existence of natural families of periodic orbits and their relation to the natural families which follow from Lyapunov's theorem are discussed. But the existence and relation of these families have not been discussed in a formal manner.
Journal ArticleDOI
Theory of the Trojan asteroids, IV
TL;DR: In this article, a long-periodic solution for the case of 1∶1 resonance in the restricted problem of three bodies to 0(m 3/2), wherem is the small mass parameter of the system, is presented.
Book ChapterDOI
The Web of Periodic Orbits at L 4
TL;DR: In this article, the results of a numerical exploration of the numerous natural families of periodic orbits associated with the L 4 equilibrium point of the restricted problem of three bodies are described and commented.
References
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Periodic orbits in the restricted three-body problem with earth-moon masses
TL;DR: Classification scheme for symmetric periodic orbits in restricted three body problem with two dimensions and earth-moon mass ratio was presented in this article, where the earth was assumed to have a constant mass.
Journal ArticleDOI
Stability of the triangular lagrangian points
TL;DR: In this paper, it was shown that the set of exceptional mass ratios for which stability remains to be proved or invalidated contains only one point besides the critical mass ratios of order two and three.
Book ChapterDOI
A Manifold of Periodic Orbits
André Deprit,Jacques Henrard +1 more
TL;DR: In this article, the authors studied the analytical manifold of periodic solutions emanating from the collinear equilibrium L sub 3 of the restricted problem of three bodies, when the mass ratio is such that the characteristic exponents at L sub 4 are equal in pair.
Journal ArticleDOI
Periodic orbits emanating from a resonant equilibrium
TL;DR: For a conservative Hamiltonian system with two degrees of freedom, in the case where the two frequencies at an equilibrium of the elliptic type are commensurable or close to being so, completely canonical transformations can be formally constructed in explicit terms under the form of Lie transforms.