The motion of the pendulum in a variable sawtooth force field is considered. For the “lower” equilibrium, the necessary stability conditions are investigated numerically, the results are presented in the form of an Ince–Strutt diagram. Using the Poincaré–Melnikov method separatrix splitting is studied analytically. Numerically, for some values of parameters, the nonlinear dynamics is studied using Poincaré maps, the regions of regular and chaotic behavior are revealed. The iterative method earlier proposed is used for the localization of periodic solutions, located inside the numerically identified “invariant tori”.

中文翻译：

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论摆在交变锯齿力场中的运动

考虑了摆在可变锯齿力场中的运动。对于“下”平衡，必要的稳定性条件进行了数值研究，结果以因斯-斯特鲁特图的形式呈现。使用 Poincaré-Melnikov 方法对分界分裂进行了分析研究。在数值上，对于某些参数值，使用庞加莱图研究了非线性动力学，揭示了规则和混沌行为的区域。早先提出的迭代方法用于定位周期解，位于数字识别的“不变环面”内。