Abstract—

The optimal control problem regarding the reorientation of an asymmetric rigid body has been investigated. The integral-quadratic functional consistent with the inertial symmetry of the body, which characterizes the total energy consumption, has been chosen as the criterion. Control is considered to be the main moment of applied external forces. An explicit description of a family of extremals for an arbitrary asymmetric rigid body has been obtained. The idea of constructing such extremals is based on the study of spatio-temporal deformations for solutions of Euler differential equations of a rigid body’s free rotation.

中文翻译：

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非对称旋转体重新定向最优控制问题中的极值

摘要-

研究了关于不对称刚体重新定向的最佳控制问题。选择与总体惯性对称一致的积分二次函数作为标准，该函数表征了总能量消耗。控制被认为是施加外力的主要时刻。已获得对任意不对称刚体的极端家族的明确描述。构造这样的极值的思想是基于时空变形的研究，以求解刚体自由旋转的欧拉微分方程。