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Sur un invariant intégral du problème des n corps: Conséquence de l'homogénéité du potentiel

Published online by Cambridge University Press:  14 August 2015

L. Losco
L. Losco*
Affiliation:
Laboratoire de Mécanique Théorique, Université de Besançon, 25030 Besançon Cédex, France

Abstract

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An integral invariant is a generalization of first integrals to differential forms. Although this mathematical technique is more difficult, the integral invariants allow to obtain new properties for systems which have already well-known first integrals. Integral invariant of first order correspond to a ‘local first integral’ near any solution of motion. In this work I obtain an ‘11th local first integral’ for the gravitational n-body problem, or any homogeneous n-body problem as planetary systems. As this local first integral contains a secular term, a discussion of the stability is obtained. The integral invariant is used for the construction of very particular solutions (Levi Civita's or Poincaré's singular solutions). These solutions realize conditional maximum or minimum of the contraction of the system.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 62: The Stability of the Solar System , 1974 , pp. 249 - 255
Copyright
Copyright © Reidel 1974 

References

Références

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