This paper studies the attitude dynamics of a rigid body in a Keplerian orbit. We show that the use of Classical Rodrigues Parameters for the attitude motion of the rigid body subject to gravity-gradient torques enables us to characterize the equilibria associated with the rotational motion about its mass center. A parametric study of the stability of equilibria is conducted to show that large oscillations are induced due to the energy exchange between the pitch and roll–yaw motions, specifically near the 2:1 resonant commensurability regions. A visualization tool is developed to study these pitch oscillations and gain insight into the rigid body motion near internal resonance conditions. A measure of coupling between the pitching and roll–yaw motions is developed to quantify the energy exchange utilizing information from the state transition matrix.

中文翻译：

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刚体在开普勒运动中的姿态动力学

本文研究了开普勒轨道上刚体的姿态动力学。我们表明，将经典罗德里格斯参数用于受重力梯度扭矩影响的刚体的姿态运动，使我们能够表征与围绕其质心的旋转运动相关的平衡。对平衡稳定性的参数研究表明，由于俯仰和横滚偏航运动之间的能量交换，特别是在 2:1 共振可公度区域附近，会引起大振荡。开发了一种可视化工具来研究这些俯仰振荡并深入了解内部共振条件附近的刚体运动。