The Principle of Least Action and Fundamental Solutions of Mass-Spring and N-Body Two-Point Boundary Value Problems
The Principle of Least Action and Fundamental Solutions of Mass-Spring and N-Body Two-Point Boundary Value Problems
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DOI：
10.1137/130921908
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
W. McEneaney;P. Dower
中科院分区：
文献类型：
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作者：
W. McEneaney;P. Dower
利用最小作用量原理研究了保守系统的两点边值问题。通过基本解与与终端数据有关的代价函数的幂等卷积，将两点边值问题转化为初值问题。将经典质量-弹簧问题作为一个简单的例子包括在内。还研究了万有引力作用下的$N$-体问题。在这里，最小行动原则最优控制问题被转化为一个微分对策，对手在一组索引的二次曲面上最大化，以产生引力势。得到的解是Riccati方程的指标解集合。
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 sets of solutions of Riccati equations.