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On Topological Stability in the General Three and Four-Body Problem

Published online by Cambridge University Press:  12 April 2016

A. Milani  and
A.M. Nobili
A. Milani
Affiliation:
Department of Astronomy, Glasgow University, U.K.
A.M. Nobili
Affiliation:
Department of Astronomy, Glasgow University, U.K.

Extract

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By simple symmetry and change-of-scale considerations the topology of the level manifolds of the classical integrals of the N-body problem is shown to depend only on the value of the integral z = c2h (total angular momentum squared times total energy). For every hierarchical structure given to the N bodies the problem can be described as a set of N-l perturbed two-body problems by means of a fitted Jacobian coordinate system; in this setting the Easton inequality, relating potential, momentum of inertia and the z integral, is easily rederived. For N=3 the confinement conditions due to this inequality can be described, in a pulsating synodic reference system, as level lines of a modified potential function on a plane.

Type
Part V - Trapped Motion in the Three-Body Problem
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 301 - 315
Copyright
Copyright © Reidel 1983

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