THE PRINCIPLE OF LEAST ACTION AND FUNDAMENTAL SOLUTIONS OF MASS-SPRING AND N-BODY TWO-POINT BOUNDARY VALUE PROBLEMS
William M McEneaney, Peter M Dower
SIAM Journal on Control and Optimization | SIAM PUBLICATIONS | Published : 2015
Two-point boundary value problems for conservative systems are studied in the context of the least action principle. One obtains a fundamental solution, whereby two-point boundary value problems are converted to initial value problems via an idempotent convolution of the fundamental solution with a cost function related to the terminal data. The claßical maß-spring problem is included as a simple example. The N-body problem under gravitation is also studied. 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. Solutions are obtained as indexed s..View full abstract
This research was partially supported by grants from AFOSR and the Australian Research Council. A condensed, preliminary version of this paper appeared in the principle of least action and solution of two-point boundary value problems on a limited time horizon, in 2013 Proceedings of the Conference on Control and its Applications, SIAM, Philadelphia, 2013 .