Stability of the Inverted Pendulum—A Topological Explanation
Stability of the Inverted Pendulum—A Topological Explanation
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倒立摆的稳定性——拓扑解释
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
M. Levi
中科院分区：
文献类型：
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作者：
M. Levi
给出了倒立摆悬点发生垂直周期振荡时稳定性的解释和证明。这个论点的主要思想是拓扑学的；事实证明，只需使用关于系统的非常粗略的定性信息，就可以很容易地证明稳定制度的存在。更准确地说，设n是钟摆在一个强迫周期内变为垂直的次数。如果n随着参数$\Mu$的变化而变化大于4，则对于$\Mu$的中间值的开放区间，摆将是稳定的。
An explanation and a proof of stability of the inverted pendulum whose suspension point undergoes vertical periodic oscillations is given. The main idea of the argument is topological; as it turns out, existence of stable regimes can be proven with little effort using only very crude qualitative information about the system. More precisely, let n be the number of times the pendulum becomes vertical during one forcing period. If n changes by more than 4 with the change of a parameter $\mu $, then for an open interval of intermediate values of $\mu $ the pendulum will be stable.