The Principle of Least Action and Solution of Two-Point Boundary Value Problems on a Limited Time Horizon

Abstract

Two-point boundary problems for conservative systems are studied in the context of the least action principle. The emphasis is on the N -body problem under gravitation. There, the least action principle optimal control problem is converted to a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. For problems where the time-duration is below a specified bound, fundamental solutions are obtained as indexed sets of solutions of Riccati equations.