Abstract—

Given a heavy rigid body with one fixed point, we investigate the problem of orbital stability of its periodic motions. Based on the analysis of the linearized system of equations of perturbed motion, the orbital instability of the pendulum rotations is proved. In the case of pendulum oscillations, a transcendental situation occurs, when the question of stability cannot be solved using terms of an arbitrarily high order in the expansion of the Hamiltonian of the equations of perturbed motion. It is proved that the pendulum oscillations are orbitally unstable for most values of the parameters.

中文翻译：

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赫斯情况下刚体摆运动的轨道稳定性

摘要-

给定一个具有一个固定点的重刚体，我们研究其周期性运动的轨道稳定性问题。通过对线性化微扰运动方程组的分析，证明了摆旋转的轨道不稳定性。在摆振荡的情况下，当稳定性问题无法使用扰动运动方程的哈密顿量展开式中的任意高阶项来解决时，就会出现超越情况。事实证明，对于大多数参数值，摆振荡是轨道不稳定的。