Clustering motions in N-body systems - free-fall motions in the Gaussian three-body problem

Miki Nakato, Yoji Aizawa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Clustering motions are typical and universal phenomena in N-body systems. Basic mechanisms leading to escaping and/or to trapping of particles are pursued in the analysis of a global structure for the three-body problem. The global structure of the three-body problem is numerically studied under the short range Gaussian interaction potential. As the Gaussian potential does not have any singularities at zero distance, we can avoid the computational errors in the long time simulations. Main concerns are the analysis of the collinear three-body problem, and the result compared with the case of gravitational potential. The distributions of periodic orbits are precisely searched and their stability is determined by the linear stability analysis. The collapsing of quasi-periodic motions is correlated to the destabilization of the three-body cluster in the case of the free-fall motions, and that the boundary for the collapsing tori displays fractal curves. Finally the escape diagram for two-dimensional three-body problems are discussed in comparison with the case of gravitational potential, where the remarkable difference near the triple collision is pointed out.

Original languageEnglish
Pages (from-to)171-185
Number of pages15
JournalChaos, Solitons and Fractals
Volume11
Issue number1
DOIs
Publication statusPublished - 2000 Jan

Fingerprint

Three-body Problem
free fall
three body problem
Clustering
Motion
Collapsing
gravitational fields
Quasi-periodic Motion
Linear Stability Analysis
Collinear
destabilization
Trapping
Periodic Orbits
escape
Fractal
fractals
Torus
Diagram
Collision
trapping

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics

Cite this

Clustering motions in N-body systems - free-fall motions in the Gaussian three-body problem. / Nakato, Miki; Aizawa, Yoji.

In: Chaos, Solitons and Fractals, Vol. 11, No. 1, 01.2000, p. 171-185.

Research output: Contribution to journalArticle

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