In the previous works by the authors, an efficient method of control of the inversion of the spinning spacecraft was proposed. This method was prompted by the Dzhanibekov’s Effect or Tennis Racket Theorem, which are often seen by many as odd or even mysterious. For the spacecraft, initially undergoing periodic flipping motion, proposed method allows to completely stop these flips by transferring the unstable motion into the regular stable spin. Similarly, the method allows activation of the flipping motion of the spacecraft, which is initially undergoing its stable spin. In this paper, spacecraft designs, which have inertial morphing capabilities, are considered and their advantages are further investigated. For general formulation, the ability of the spacecraft to change its inertial properties, associated with all three principal axes of inertia, are assumed. For simulation of these types of spacecraft systems, extended Euler’s equations are used and peculiar dynamics of the spacecraft is illustrated with a several study cases. Complex spacecraft attitude dynamics manoeuvres, using geometric interpretation, employing angular momentum spheres and kinetic energy ellipsoids, are considered in detail. Contributions of the inertial morphing to the changes of the shape of the kinetic energy ellipsoid are demonstrated and are related to the resultant various feature manoeuvres, including inversion and re-orientation. A method of reduction of the compound rotation of the spacecraft into a single stable predominant rotation around one of the body axes was proposed. This is achieved via multi-stage morphing and employing proposed instalment into separatrices. Implementation of the morphing control capabilities are discussed. For the periodic inversion motions, calculation of the periods of the flipping motion, based on the complete elliptic integral of the first kind, is performed. Flipping periods for various combinations of inertial properties of the spacecraft are presented in a systematic way. This paper discusses strategies to the increase or reduction the flipping and/or wobbling motions. A discovered asymmetric ridge of high periods for peculiar combinations of the inertial properties is discussed in detail. Numerous examples are illustrated with animations in virtual reality, facilitating explanation of the analysis and control methodologies to a wide audience, including specialists, industry and students.

中文翻译：

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利用惯性变形增强旋转航天器的姿态动力学能力

在作者之前的工作中，提出了一种控制旋转航天器反转的有效方法。这种方法是由 Dzhanibekov 效应或网球拍定理提出的，许多人经常认为这很奇怪甚至神秘。对于最初经历周期性翻转运动的航天器，所提出的方法允许通过将不稳定运动转变为常规稳定旋转来完全停止这些翻转。类似地，该方法允许激活航天器的翻转运动，该航天器最初正在经历其稳定的旋转。在本文中，考虑了具有惯性变形能力的航天器设计，并进一步研究了它们的优势。对于一般公式，航天器改变其惯性特性的能力，与所有三个惯性主轴相关，假定。为了模拟这些类型的航天器系统，使用了扩展的欧拉方程，并通过几个研究案例说明了航天器的特殊动力学。复杂的航天器姿态动力学机动，使用几何解释，采用角动量球和动能椭球，被详细考虑。惯性变形对动能椭球形状变化的贡献得到了证明，并与由此产生的各种特征操作有关，包括反转和重新定向。提出了一种将航天器的复合旋转减少为围绕其中一个体轴的单一稳定主导旋转的方法。这是通过多阶段变形和将建议的装置应用到分离中来实现的。讨论了变形控制能力的实现。对于周期反演运动，基于第一类完全椭圆积分计算翻转运动的周期。系统地介绍了航天器惯性特性的各种组合的翻转周期。本文讨论了增加或减少翻转和/或摆动运动的策略。详细讨论了由于惯性特性的特殊组合而发现的不对称高周期脊。许多示例都以虚拟现实中的动画进行说明，便于向包括专家、行业和学生在内的广大受众解释分析和控制方法。基于第一类完全椭圆积分计算翻转运动的周期。系统地介绍了航天器惯性特性的各种组合的翻转周期。本文讨论了增加或减少翻转和/或摆动运动的策略。详细讨论了由于惯性特性的特殊组合而发现的不对称高周期脊。许多示例都以虚拟现实中的动画进行说明，便于向包括专家、行业和学生在内的广大受众解释分析和控制方法。基于第一类完全椭圆积分计算翻转运动的周期。系统地介绍了航天器惯性特性的各种组合的翻转周期。本文讨论了增加或减少翻转和/或摆动运动的策略。详细讨论了由于惯性特性的特殊组合而发现的不对称高周期脊。许多示例都用虚拟现实中的动画进行了说明，便于向包括专家、行业和学生在内的广大受众解释分析和控制方法。系统地介绍了航天器惯性特性的各种组合的翻转周期。本文讨论了增加或减少翻转和/或摆动运动的策略。详细讨论了由于惯性特性的特殊组合而发现的不对称高周期脊。许多示例都用虚拟现实中的动画进行了说明，便于向包括专家、行业和学生在内的广大受众解释分析和控制方法。系统地介绍了航天器惯性特性的各种组合的翻转周期。本文讨论了增加或减少翻转和/或摆动运动的策略。详细讨论了由于惯性特性的特殊组合而发现的不对称高周期脊。许多示例都用虚拟现实中的动画进行了说明，便于向包括专家、行业和学生在内的广大受众解释分析和控制方法。