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Masses for which triple collision is regularizable

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Abstract

We consider the regularization by continuity w.r.t. initial conditions (geometric or Easton method) which has a sense both in physical and computational aspects. Using the idea of triple collision manifold of McGehee we study the values of masses for which the invariant manifolds of equilibrium points coincide. Local analytical equations are continuated numerically. So one gets the masses satisfying a necessary condition. Again analytically we discuss the neighbourhood of t.c.m. at the equilibrium points. A necessary and sufficient condition in terms of integrals along invariant manifolds is found for the rectilinear case. This can be tested for the masses obtained above. Only a countable (symmetric) set of masses remains. Then, due to errors in physical measurements or numerical integrations we can never expect a regular behaviour. Extension to the planar case is also taken into account.

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Authors and Affiliations

  1. Facultat de Matemàtiques Universitat de Barcelona, Spain

    Carles Simó

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  1. Carles Simó
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Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.

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Simó, C. Masses for which triple collision is regularizable. Celestial Mechanics 21, 25–36 (1980). https://doi.org/10.1007/BF01230243

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  • DOI: https://doi.org/10.1007/BF01230243

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