Motions close to escapes in the rhomboidal four body problem

Details Motions close to escapes in the rhomboidal four body problem Motions close to escapes in the rhomboidal four body problem

Nov 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..57..411l&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 57, no. 3, p. 411-437

Mathematics

4

Celestial Mechanics, Computerized Simulation, Escape Velocity, Four Body Problem, Orbital Mechanics, Manifolds (Mathematics), Mass Ratios, Reversed Flow, Rhomboids

Scientific paper

In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analysis, we show certain transversal intersections of the invariant manifolds of parabolic orbits. We then introduce Symbolic Dynamics when the mass ratio is small, and when it is close to one. In the first case the escapes or captures predominate in the direction of one of the diagonals of the rhombus, while in the second case we find solutions escaping or being captured in the direction of both possible diagonals.

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