Sur un Invariant INTÉGRAL du PROBLÉME des N Corps: CONSÉQUENCE de L'HOMOGÉNÉITÉ du Potentiel
Abstract
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 wellknown first integrals. Integral invariants of first order correspond to a 'local first integral' near any solution of motion. In this work, an '11th local first integral' for the gravitational nbody problem, or any homogeneous nbody problem as planetary systems, is obtained. As this local first integral contains a secular term, a discussion of the stability follows. The integral invariant is used for the construction of very particular solutions (Levi Civita's or Poincare's singular solutions). These solutions realize conditional maximum or minimum of the contraction of the system.
 Publication:

Stability of the Solar System and of Small Stellar Systems
 Pub Date:
 1974
 Bibcode:
 1974IAUS...62..249L
 Keywords:

 Celestial Mechanics;
 Invariance;
 Many Body Problem;
 Potential Fields;
 Classical Mechanics;
 Homogeneity;
 Integral Calculus;
 Motion Stability;
 Orbit Perturbation;
 Planetary Systems;
 Solar System;
 Three Body Problem;
 Astronomy