Abstract

In the quaternionic setting, we consider the problem of optimal control of a spatial attitude maneuver of a spacecraft viewed as a rigid body with one symmetry axis without a constraint on the control function. For the optimality criterion we use a functional combining the time and energy spent on turning the spacecraft. Based on the Pontryagin maximum principle for this problem, new analytical solutions are obtained in the classes of conical and generalized conical motions. Numerical examples are given.

中文翻译：

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组合函数下轴对称航天器姿态机动问题的解析解

摘要

在四元数设置中，我们考虑航天器空间姿态机动的最优控制问题，该航天器被视为具有一个对称轴的刚体，对控制函数没有约束。对于最优性标准，我们使用了一个函数，结合了转动航天器所花费的时间和能量。基于此问题的庞特里亚金极大值原理，在圆锥运动和广义圆锥运动的类别中获得了新的解析解。给出了数值例子。