The principle of least action and two-point boundary value problems in orbital mechanics
The principle of least action and two-point boundary value problems in orbital mechanics
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轨道力学中最小作用原理与两点边值问题
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
W. McEneaney
中科院分区：
文献类型：
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作者：
S. Han;W. McEneaney
考虑轨道力学中的一个两点边值问题（TPBVP），该问题涉及一个小天体（例如，航天器或小行星）和N个较大的天体。最小作用原理TPBVP制定转化为一个初始值问题，通过添加一个适当的终端成本的行动功能。后者制定是用来获得一个基本的解决方案，这可能是用来解决TPBVP在一定的类内的各种边界条件。特别是，凸对偶的方法允许人们将最小作用量原理解释为微分博弈，其中对方玩家在一组二次指数上最大化以产生引力势。基本解作为一组相关的Riccati方程的解而得到。
We consider a two-point boundary value problem (TPBVP) in orbital mechanics involving a small body (e.g., a spacecraft or asteroid) and N larger bodies. The least action principle TPBVP formulation is converted into an initial value problem via the addition of an appropriate terminal cost to the action functional. The latter formulation is used to obtain a fundamental solution, which may be used to solve the TPBVP for a variety of boundary conditions within a certain class. In particular, the method of convex duality allows one to interpret the least action principle as a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. The fundamental solution is obtained as a set of solutions of associated Riccati equations.