具有干摩擦的双弹簧振子的全局动力学
Global Dynamics of Double-Spring Oscillators with Dry Friction
DOI: 10.12677/AAM.2025.142064, PDF,    科研立项经费支持
作者: 毛睿婕：长沙理工大学数学与统计学院，湖南 长沙
关键词: 干摩擦；弹簧振子；Filippov系统；Lyapunov函数；LaSalle不变原理；Dry Friction； Spring Oscillator； Filippov System； Lyapunov Functions； LaSalle Invariant Principle
摘要: 本文研究了一类具有干摩擦的双弹簧振子模型的全局动力学。首先，根据牛顿第二定律建立具有 干摩擦的双弹簧振子模型的微分方程，求得系统的平衡点。接下来, 通过 Filippov 理论证明了系 统存在一个平衡点集或三个平衡点集。 然后，再根据非光滑的 Lyapunov 函数和集值导数以及 LaSalle 不变原理等相关理论讨论了不同情况下平衡点集的渐近稳定性。最后，绘制分岔图分析了 系统的分岔情况，并选取合适的参数进行数值模拟验证结论。
Abstract: In this paper, the global dynamics of a class of double-spring oscillator model with dry friction is studied. Firstly, according to Newton’s second law, the differential equation of the double-spring oscillator model with dry friction is established to obtain the equilibrium point of the system. Next, the Filippov correlation theory proves that there is one equilibrium set or three equilibrium sets in the system. Then, the asymptotic stability of the equilibrium set in different cases is discussed according to the non-smooth Lyapunov function, the set-valued derivative and LaSalle’s invariant principle. Finally, the bifurcation diagram is drawn to analyze the bifurcation of the system, and the appropriate parameters are selected for numerical simulation to verify the conclusion.
文章引用：毛睿婕. 具有干摩擦的双弹簧振子的全局动力学[J]. 应用数学进展, 2025, 14(2): 202-216. https://doi.org/10.12677/AAM.2025.142064

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