应用数学和力学2026，Vol.47Issue(8)：1060-1067,8.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
Dynamical Modeling and Stability Analysis of Periodic Orbits for Bouncing Ellipsoids
摘要
Abstract
The bouncing ball model has garnered significant attention since the 1 940 s,with scholars extensive-ly 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 quintes-sential 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 per-fectly 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 find-ings,thereby substantiating the robustness of the proposed method.关键词
弹跳椭球/碰撞/周期轨道/稳定性Key words
bouncing ellipsoid/collision/periodic orbit/stability分类
数理科学引用本文复制引用
万宽,张晓明,王永萍,乐源,李登辉..弹跳椭球的动力学建模与周期轨道稳定性分析[J].应用数学和力学,2026,47(8):1060-1067,8.基金项目
国家自然科学基金(12202168 （）
12302015 （）
12362002) （）
