Journal article

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

Abstract

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..

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Grants

Funding Acknowledgements

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 [23].