We study the dynamics of a simple pendulum attached to the center of mass of a satellite in an elliptic orbit. We consider the case where the pendulum lies in the orbital plane of the satellite. We find two linearly stable equilibrium positions for the Hamiltonian system describing the problem and study their parametric stability by constructing the boundary curves of the stability/instability regions.

中文翻译：

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椭圆轨道上变长摆的参数稳定性

我们研究了附加在椭圆轨道上卫星质心的简单摆的动力学。我们考虑摆在卫星轨道平面上的情况。我们找到了描述问题的哈密顿系统的两个线性稳定平衡位置，并通过构造稳定/不稳定区域的边界曲线来研究它们的参数稳定性。