151. How the Method of Minimization of Action Avoids Singularities
- Author
-
C. Marchal
- Subjects
Discontinuity (linguistics) ,Mathematical optimization ,Singularity ,Bounded function ,Mathematical analysis ,Gravitational singularity ,Boundary value problem ,Minification ,Interference (wave propagation) ,Action (physics) ,Mathematics - Abstract
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.
- Published
- 2002
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