The "not quite" inverted pendulum
The "not quite" inverted pendulum
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“不完全”的倒立摆
DOI：
10.1142/s0218127499000158
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发表时间：
1999
影响因子：
2.2
通讯作者：
D. J. Sudor
中科院分区：
文献类型：
--
作者：
S. Bishop;D. J. Sudor
300多年来，平面摆一直被用作简单振荡器的一个例子，伽利略和惠更斯在历史上做出了显著的贡献。最初，人们的兴趣集中在从稳定的悬挂位置产生的微小位移上，以具体确定振荡周期。最近，由于对枢轴点的周期性强迫，人们的注意力转向了更大的幅度和混乱的运动。为了解释实验观察到的行为，我们在这里研究了正弦驱动的摆的稳定倒解的存在性，首先是由纯垂直力驱动的，然后是通过给予系统小倾斜而由几乎垂直的力驱动的。考虑了一个有效的势函数，为数值模拟提供了分析依据。
The planar pendulum has been used as an example of a simple oscillator for over 300 years with notable historical contributions by Galileo and Huygens. Initially interest was focused on small displacements from the stable hanging position specifically to determine the period of oscillation. More recently attention has switched to larger amplitude and chaotic motions as a consequence of periodic forcing to the pivot point. To explain experimentally observed behavior, we investigate here the existence of stable inverted solutions of a pendulum sinusoidally driven, in the first instance by a purely vertical force and then by an almost vertical force by giving a small tilt to the system. An effective potential function is considered to provide analytical justification of the numerical simulations.