We consider a planar pendulum with an oscillating suspension point and with the bob carrying an electric charge \(q\) . The pendulum oscillates above a fixed point with a charge \(Q.\) The dynamics is studied as a system in the small parameter \(\epsilon\) given by the amplitude of the suspension point. The system depends on two other parameters, \(\alpha\) and \(\beta,\) the first related to the frequency of the oscillation of the suspension point and the second being the ratio of charges. We study the parametric stability of the linearly stable equilibria and use the Deprit – Hori method to construct the boundary surfaces of the stability/instability regions.

我们考虑一个平面摆，该摆具有一个振荡的悬挂点，并且摆锤带有电荷 \（q \） 。摆锤在固定点上方以电荷\（Q. \）振荡 。以悬架点的振幅给定 的小参数\（\ epsilon \）作为系统来研究动力学 。该系统取决于其他两个参数， \（\ alpha \） 和 \（\ beta，\） ，第一个与悬挂点的振荡频率有关，第二个与电荷比率有关。我们研究了线性稳定平衡的参数稳定性，并使用Deprit-Hori方法构造了稳定性/不稳定性区域的边界面。