Dynamical Modeling and Stability Analysis of Periodic Orbits for Bouncing Ellipsoids

Wan Kuan; Zhang Xiaoming; Wang Yongping; Le Yuan; Li Denghui

doi:10.21656/1000-0887.460166

Volume 47 Issue 8

Aug. 2026

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Wan Kuan, Zhang Xiaoming, Wang Yongping, Le Yuan, Li Denghui. Dynamical Modeling and Stability Analysis of Periodic Orbits for Bouncing Ellipsoids[J]. Applied Mathematics and Mechanics, 2026, 47(8): 1060-1067. doi: 10.21656/1000-0887.460166

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Dynamical Modeling and Stability Analysis of Periodic Orbits for Bouncing Ellipsoids

doi: 10.21656/1000-0887.460166

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

Received Date: 2025-09-19
Rev Recd Date: 2025-12-01

Available Online: 2026-07-30

Publish Date: 2026-08-01

Abstract

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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References(13)

References

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