弹跳椭球的动力学建模与周期轨道稳定性分析

万宽; 张晓明; 王永萍; 乐源; 李登辉

doi:10.21656/1000-0887.460166

弹跳椭球的动力学建模与周期轨道稳定性分析

doi: 10.21656/1000-0887.460166

1. 西南交通大学力学与航空航天学院，成都 610031;
2. 苏州工学院数学与统计学院，江苏常熟 215500

基金项目:

12362002)

国家自然科学基金(12202168

12302015

详细信息

作者简介:
万宽(1999—)，男，硕士生(E-mail: wankuan2023@163.com)；乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).

通讯作者:
乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).

中图分类号: O322
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- 文章访问数: 17
- HTML全文浏览量: 6
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2025-09-19
- 修回日期: 2025-12-01
- 网络出版日期: 2026-07-30
- 刊出日期: 2026-08-01

Dynamical Modeling and Stability Analysis of Periodic Orbits for Bouncing Ellipsoids

1. School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, P.R. China;
2.School of Mathematics and Statistics, Suzhou University of Technology,Changshu, Jiangsu 215500, P.R. China

Funds:

12362002)

The National Science Foundation of China(12202168

12302015

摘要

摘要: 弹跳球模型早在20世纪40年代便有学者进行研究，其描述一个质点在重力的作用下，与一个周期振动的板发生碰撞并往复运动的动力学过程.混沌理论与非光滑动力学发展至今，该模型是诸多理论应用的试验田.本文考虑弹跳椭球模型，推导了椭球在完全弹性碰撞条件下的运动方程，得到了系统的守恒量和平凡周期轨道的稳定性条件，并在数值上验证了主要结果.
- 弹跳椭球 /
- 碰撞 /
- 周期轨道 /
- 稳定性
Abstract: The bouncing ball model has garnered significant attention since the 1 940 s, with scholars extensively investigating the dynamics of a point mass undergoing collisions with a periodically oscillating surface under gravitational influence. As the chaos theory and nonsmooth dynamics evolved, this model emerged as a quintessential testbed for the application of these theoretical frameworks. Herein, the inquiry was extended to the bouncing ellipsoid model. The equations of motion were meticulously derived for an ellipsoid experiencing perfectly elastic collisions. The analysis yields the conserved quantities of the system and elucidates the stability conditions of its trivial periodic orbits. Furthermore, the numerical simulations corroborate the theoretical findings, thereby substantiating the robustness of the proposed method.
- bouncing ellipsoid /
- collision /
- periodic orbit /
- stability

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参考文献(13)

史美娇, 徐慧东, 张建文. 双侧弹性约束悬臂梁的非光滑擦边动力学[J]. 应用数学和力学, 2022,43(6): 619-630.

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[3]马成, 朱喜锋, 郑冬, 等. 一类非线性约束下单自由度碰撞系统的动力学特性[J]. 机械强度, 2025,47(3): 82-89.(Ma Cheng, Zhu Xifeng, Zheng Dong, et al. Dynamic characteristics of a class of single-degree-of-freedom collision system under nonlinear constraint[J]. Journal of Mechanical Strength,2025,47(3): 82-89. (in Chinese))

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弹跳椭球的动力学建模与周期轨道稳定性分析

doi: 10.21656/1000-0887.460166

作者简介:
万宽(1999—)，男，硕士生(E-mail: wankuan2023@163.com)；乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).

通讯作者:
乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).

计量

Dynamical Modeling and Stability Analysis of Periodic Orbits for Bouncing Ellipsoids

计量

目录

留言板

弹跳椭球的动力学建模与周期轨道稳定性分析

doi: 10.21656/1000-0887.460166

作者简介: 万宽(1999—)，男，硕士生(E-mail: wankuan2023@163.com)；乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).

通讯作者: 乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).

计量

出版历程

Dynamical Modeling and Stability Analysis of Periodic Orbits for Bouncing Ellipsoids

计量

出版历程

目录

作者简介:
万宽(1999—)，男，硕士生(E-mail: wankuan2023@163.com)；乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).

通讯作者:
乐源(1974—)，男，教授，博士，博士生导师(通信作者. E-mail: leyuan2003@sina.com).