标题： 摆的运动，由具有位置相关相位的磁激励驱动 显示英文标题

标题： Dynamics of Pendulum Forced by a Magnetic Excitation with Position-Dependent Phase

摘要： 本研究探讨了在随时间变化的磁激励下具有位置依赖相位的磁摆的动力学特性。 该系统表现出复杂的混沌和规则动力学，通过仿真和实验得到验证。 数学模型基于物理装置，包括与动态变量相位相关的磁激励转矩。 分岔分析证实了系统的丰富多稳定性，展示了周期吸引子、周期倍分岔和混沌行为。 实验验证表明数值结果与实验结果高度一致，支持了所提出模型的有效性。 本研究揭示了系统对磁相互作用变化的敏感性，为控制耦合磁摆系统中的共振能量交换提供了见解。 显示英文摘要

摘要： This study investigates the dynamics of a magnetic pendulum under time-varying magnetic excitation with a position-dependent phase. The system exhibits complex chaotic and regular dynamics, validated through simulations and experiments. The mathematical model, based on a physical setup, includes a magnetic excitation torque with phase dependence on the dynamic variable. Bifurcation analyses confirm the rich multistability of the system, showcasing periodic attractors, period-doubling bifurcations, and chaotic behavior. Experimental validation demonstrates a high agreement between numerical and experimental results, supporting the efficacy of the proposed model. The study sheds light on the system's sensitivity to changes in magnetic interaction, providing insights into controlling resonance energy exchange in coupled magnetic pendulum systems.