Abstract
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−1 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.
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© 1983 D. Reidel Publishing Company, Dordrecht, Holland
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Milani, A., Nobili, A.M. (1983). On Topological Stability in the General Three and Four-Body Problem. In: Markellos, V.V., Kozai, Y. (eds) Dynamical Trapping and Evolution in the Solar System. Astrophysics and Space Science Library, vol 106. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7214-8_34
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DOI: https://doi.org/10.1007/978-94-009-7214-8_34
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