Chaotic transfers in three- and four-body systems

Gidea, Marian; Burgos, Melissa

doi:10.1016/s0378-4371(03)00582-x

Cited by 11 publications

(8 citation statements)

References 4 publications

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“…Regularization of collisions are studied by Álvarez-Ramírez, Delgado, and Vidal in [32]. Chaotic motions were studied numerically by Gidea and Burgos in [33], and by Álvarez-Ramírez and Barrabés in [34]. Perturbative proofs of the existence of chaotic motions are found in the work of She, Cheng and Li [35,36,37], and also in the work of Alvarez-Ramírez, García, Palacián, and Yanguas [38].…”

Section: Introductionmentioning

confidence: 99%

Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

Kepley

James

2019

Celest Mech Dyn Astr

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We describe a method for computing an atlas for the stable or unstable manifold attached to an equilibrium point, and implement the method for the saddle-focus libration points of the planar equilateral restricted four body problem. We employ the method at the maximally symmetric case of equal masses, where we compute atlases for both the stable and unstable manifolds. The resulting atlases are comprised of thousands of individual chart maps, with each chart represented by a two variable Taylor polynomial. Post-processing the atlas data yields approximate intersections of the invariant manifolds, which we refine via a shooting method for an appropriate two point boundary value problem. Finally, we apply numerical continuation to some of the BVP problems. This breaks the symmetries and leads to connecting orbits for some non-equal values of the primary masses.Keywords Gravitational 4-body problem • invariant manifolds • high-order Taylor methods • automatic differentiation • numerical continuation

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Section: Introductionmentioning

confidence: 99%

Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

Kepley

James

2019

Celest Mech Dyn Astr

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“…The model under consideration can be used in studying the dynamics of planets orbiting systems of binary stars (see [14,11]), in which case the primaries have Another possible application regards mass transfers in binary stars. Mass transfer commonly occurs in tight binary star systems.…”

Section: Introductionmentioning

confidence: 99%

Geometry of Homoclinic Connections in a Planar Circular Restricted Three-Body Problem

Gidea

Masdemont

2007

Int. J. Bifurcation Chaos

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Abstract. The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L 1 between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between the one of L 1 and that of the other collinear libration points L 2 and L 3 is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

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“…Earlier models for the dynamics of a planet near a binary star system only considered the motion of the planet in a planar orbit either about one of the stars, or well outside of the binary (see [3]). Our models suggest that spatial configurations, with long term chaotic motion, are also possible (see [4]). The methods involved here could also be useful in studying the classical mechanics of spatial three-body configurations (non-zero angular momentum) of two electron atoms (see [5]).…”

Section: Introductionmentioning

confidence: 76%

Chaotic orbits in a restricted three-body problem: numerical experiments and heuristics

Gidea

Deppe

2006

Communications in Nonlinear Science and Numerical Simulation

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Chaotic transfers in three- and four-body systems

Cited by 11 publications

References 4 publications

Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

Geometry of Homoclinic Connections in a Planar Circular Restricted Three-Body Problem

Chaotic orbits in a restricted three-body problem: numerical experiments and heuristics

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