The fundamental instability of the general N-body problem

Details The fundamental instability of the general N-body problem The fundamental instability of the general N-body problem

Sep 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979muni.iafcq....m&link_type=abstract

International Astronautical Federation, International Astronautical Congress, 30th, Munich, West Germany, Sept. 17-22, 1979, 12

Mathematics

Logic

Celestial Mechanics, Many Body Problem, Motion Stability, Systems Stability, Liapunov Functions, Lipschitz Condition, Orbital Mechanics, Phase-Space Integral, Trajectory Analysis, Vector Analysis

Scientific paper

The long range stability of the general N-body problem is dicussed for small perturbations. The angular momentum equations of the trajectories employing Lipschitz integrals of motion are the main tools of the analysis. Attention is given to the topological properties of the conservative phenomena for integrals of motion and T-distance. The series of small perturbations for long range stability is examined and its application to the N-body problem is presented. It is determined that systems with many parameters do not have enough integrals of motion available to have long range stability, and an arbitrarily small sum of corrections can lead them far from their unperturbed motion.

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