钟摆模型极限环的存在性研究

发布时间：2018-05-07 06:30

本文选题：钟摆 + 极限环　；参考：《数学的实践与认识》2017年10期

【摘要】：钟摆系统是一类典型的分段光滑系统,结合Filippov系统刻画语言,解释了当钟摆无能量补充时,钟摆最终会停止在滑动集上的原因.利用数值模拟的方法,给出钟摆系统在有能量补充时,存在极限环的条件.最后,结合环域定理证明了一般的钟摆模型存在唯一稳定的极限环.
[Abstract]:Pendulum system is a typical piecewise smooth system. Combined with Filippov system description language, it explains why the pendulum will eventually stop on the sliding set when the pendulum has no energy supplement. By means of numerical simulation, the conditions for the existence of limit cycles for pendulum systems with energy supply are given. Finally, the existence of a unique stable limit cycle for a general pendulum model is proved by using the ring domain theorem.
【作者单位】：江苏大学理学院;
【分类号】：O175

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