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Action-minimizing orbits in the parallelogram four-body problem with equal masses

CHEN, Kuo-Chang

Archive for rational mechanics and analysis, 2001-07, Vol.158 (4), p.293-318 [Periódico revisado por pares]

Heidelberg: Springer

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Título:
Action-minimizing orbits in the parallelogram four-body problem with equal masses
Autor: CHEN, Kuo-Chang
Assuntos: Algorithms ; Astronomy ; Celestial mechanics (including n-body problems) ; Earth, ocean, space ; Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Fundamental astronomy ; Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations ; Physics ; Solid dynamics (ballistics, collision, multibody system, stabilization...) ; Solid mechanics
É parte de: Archive for rational mechanics and analysis, 2001-07, Vol.158 (4), p.293-318
Descrição: In this paper we prove the existence of a new periodic solution for the planar Newtonian four-body problem with equal masses. On this orbit two mass points travel on one star-shaped closed curve while the other two travel on another and have the opposite orientation. The configuration of the masses changes from square to collinear periodically and remains a parallelogram for all time. Our proof is based on a variational approach inspired by a recent work of Chenciner & Montgomery [5]. By choosing an appropriate subspace of the Sobolev space H ^sup 1^([0,T],V), where V is the configuration space, we show that the action functional restricted to this subspace attains its infimum and any minimizer solves the Newtonian four-body problem. The orbits we found are indeed extensions of these minimizers. By studying the behavior of minimizers in reduced configuration space and comparing their action with rhomboid motions, we show that these minimizers do not experience any collision.[PUBLICATION ABSTRACT]
Editor: Heidelberg: Springer
Idioma: Inglês

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Action-minimizing orbits in the parallelogram four-body problem with equal masses

CHEN, Kuo-Chang

Heidelberg: Springer

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