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

万宽^1,,
张晓明¹,
王永萍¹,
乐源^1, ,,
李登辉²

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:

国家自然科学基金 12202168

国家自然科学基金 12302015

国家自然科学基金 12362002

详细信息

作者简介:
万宽(1999—)，男，硕士生(E-mail: wankuan2023@163.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
计量
- 文章访问数: 148
- HTML全文浏览量: 54
- PDF下载量: 29
- 被引次数: 0
出版历程
- 收稿日期: 2025-09-19
- 修回日期: 2025-12-01
- 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

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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图 1 椭球体三维建模示意图

Figure 1. The 3D ellipsoid modeling schematic

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图 2 E=106时的轨道图

注   为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. The orbital diagram for E=106

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图 3 E=106时的Poincaré映射相图

注   为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. The Poincaré map phase diagram for E=106

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图 4 E=130时的轨道图

注   为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. The orbital diagram for E=130

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图 5 E=130时的Poincaré映射相图

注   为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 5. The Poincaré map phase diagram for E=130

下载: 全尺寸图片幻灯片

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