How the Method of Minimization of Action Avoids Singularities

Details How the Method of Minimization of Action Avoids Singularities How the Method of Minimization of Action Avoids Singularities

May 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cemda..83..325m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 83, Issue 1, p. 325-353 (2002).

Astronomy and Astrophysics

Astronomy

14

Method Of Minimization Of Action, N-Body, Optimization

Scientific paper

The method of minimization of action is a powerful technique of proving the existence of particular and interesting solutions of the n-body problem, but it suffers from the possible interference of singularities. The minimization of action is an optimization and, after a short presentation of a few optimization theories, our analysis of interference of singularities will show that: (A) An n-body solution minimizing the action between given boundary conditions has no discontinuity: all n-bodies have a continuous and bounded motion and thus all eventual singularities are collisions; (B) A beautiful extension of Lambert's theorem shows that, for these minimizing solutions, no double collision can occur at an intermediate time; (C) The proof can be extended to triple and to multiple collisions. Thus, the method of minimization of action leads to pure n-body motions without singularity at any intermediate time, even if one or several collisions are imposed at initial and/or final times. This method is suitable for non-infinitesimal masses only. Fortunately, a similar method, with the same general property with respect to the singularities, can be extended to n-body problems including infinitesimal masses.

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