标题： 单摆非线性动力学分析，使用磁荷相互作用模型和实验拟合相互作用模型，该模型由磁场驱动 显示英文标题

标题： Analysis of the nonlinear dynamics of a single pendulum driven by a magnetic field using the magnetic charges interaction model and the experimentally fitted interaction model

摘要： 在本工作中，我们从理论上和实验上分析了由线圈-磁铁相互作用驱动的磁摆的非线性动力学。 磁性元件之间的力以及作用在摆上的扭矩是通过磁荷相互作用模型和实验拟合的相互作用模型推导出来的。 这使得两种模型之间能够进行比较。 线圈中的电流首先被取为正弦电流，然后被取为方波电流。 对每个相互作用模型的结构进行了比较，结果表明它们给出定性相似的特性。 采用谐波平衡法来近似摆的频率响应，从而得到对称和非对称或单侧（亚势阱）振荡。 绘制了双参数分岔图，显示了不同的动力学行为，考虑电流幅度和频率作为控制参数。 我们的理论结果与实验结果之间存在良好的一致性。 显示英文摘要

摘要： In this work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum driven by a coil-magnet interaction. The force between the magnetic elements and the resulting torque on the pendulum are derived using both the magnetic charges interaction model and the experimentally fitted interaction model. This enables the comparison between the two models. The current in the coil is taken first as a sinusoidal current and then as a square current. The comparison of the structure of each interaction model is conducted and it appears that they give qualitatively similar characteristics. The harmonic balance method is used to approximate the frequency responses of the pendulum leading to both symmetric and asymmetric or one-side (intrawell) oscillations. The two-parameters bifurcation diagrams are plotted showing the different dynamical behaviors considering the current amplitude and frequency as the control parameters. Good agreements are found between our theoretical results and experimental ones.