倾斜平面上非线性不连续振子的全局动力学
Global Dynamics of an Irrational Nonlinear Discontinuous Oscillator on an Inclined Plane
DOI: 10.12677/AAM.2023.1210419, PDF, 下载: 109  浏览: 146 
作者: 夏珏武：长沙理工大学数学与统计学院，湖南 长沙
关键词: SD振子；平衡集；干摩擦；SD Oscillator； Equilibrium Set； Dry Friction
摘要: 本文的目的是将平面上带干摩擦的SD振子的动力学结果推广至斜面上。 分析结果表明，系统会有 一个或两个平衡集。 并通过非光滑李雅普诺夫函数证明了平衡集的稳定性。 最后我们给出了数值 模拟图来说明动力学并验证结果。
Abstract: The purpose of this article is to extend the dynamic results of SD oscillators with dry friction on a plane to an inclined plane. The analysis results indicate that the system will have one or two equilibrium sets. And the stability of the equilibrium set was proved through non smooth Lyapunov functions. Finally, we provided numerical simulations to illustrate the dynamics and validate the results.
文章引用：夏珏武. 倾斜平面上非线性不连续振子的全局动力学[J]. 应用数学进展, 2023, 12(10): 4255-4263. https://doi.org/10.12677/AAM.2023.1210419

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