Tranversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem
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In this paper, the authors considered the restricted three-body problem for values of the Jacobi constant C near the value C 2 associated to the Euler critical point L 2, and derived asymptotical expressions of the invariant manifolds for C ≲ C 2 and μ ≳ 0.About:
This article is published in Journal of Differential Equations.The article was published on 1985-06-15 and is currently open access. It has received 150 citations till now. The article focuses on the topics: Invariant (mathematics) & Homoclinic orbit.read more
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Journal ArticleDOI
Heteroclinic Connections Between Periodic Orbits and Resonance Transitions in Celestial Mechanics
TL;DR: The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L(1) and the other around L(2), with the two periodic orbits having the same energy.
Book
Dynamical Systems, the Three-Body Problem and Space Mission Design
TL;DR: In this article, the existence of a heteroclinic connection between pairs of equal energy periodic orbits around two of the libration points is shown numerically and applied to resonance transition and the construction of orbits with prescribed itineraries.
Book ChapterDOI
Low Energy Transfer to the Moon
TL;DR: In this article, the authors apply the dynamical systems techniques developed in earlier work to reproduce systematically a Hiten-like mission, and approximate the Sun-Earth-Moon-spacecraft 4-body system as two 3-body systems.
Journal ArticleDOI
Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
TL;DR: The theory and application of homoclinic orbits to equilibria in reversible continuous-time dynamical systems, where the homOClinic orbit and the equilibrium are both reversible, are reviewed, including even-order reversible systems in four or more dimensions.
Journal ArticleDOI
The dynamics around the collinear equilibrium points of the RTBP
Gerard Gómez,J. M. Mondelo +1 more
TL;DR: In this paper, an extended neighborhood of the collinear equilibrium points of the restricted three body problem is analyzed using numerical tools for the determination of periodic orbits and invariant 2D tori.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Theory of Orbits.
TL;DR: In this paper, a book on theory of orbits covering restricted problem of three bodies, two bodies in rotating coordinate system and periodic orbits is presented. But it does not cover the problem of periodic orbits.
Journal ArticleDOI
Stable and Random Motions in Dynamical Systems
Jürgen Moser,Donald G. Saari +1 more