耦合球面摆的数值分析  

Numericalanalysis of the coupled spherical pendulums

作　　者：张锋俞 刘芬 吕英波 张鹏 关成波 ZHANG Feng-yu;LIU Fen;LU Ying-bo;ZHANG Peng;GUAN Cheng-bo(School of Space Science and Physics,Shandong University,Weihai,Shandong 264209,China)

机构地区：[1]山东大学(威海)空间科学与物理学院,山东威海264209

出　　处：《大学物理》2025年第2期81-87,共7页College Physics

基　　金：山东大学教改(Y2022040,Z2023033,Z2022006,Y2023025);山东省自然科学基金ZR2022MA017;山东省本科教改M2021322。

摘　　要：球面摆是在重力作用下绕悬点做定点转动的单摆,其质心被约束在球面上运动.本文首先讨论了单个球面摆运动方程的数值模拟及其摆动周期与初始条件的关系;然后对耦合球面摆系统进行了数值求解,讨论了弹簧劲度系数对耦合摆能量传递的影响,通过傅里叶变换给出各组分能量的频谱分布,利用轨迹图和庞加莱截面阐明了大摆角非线性运动中的混沌现象.The spherical pendulum is a single pendulum that rotates around the suspension point under the action of gravity,and hence its center of mass is constrained on a sphere.In this paper,we numerically simulate the motion of a single spherical pendulum,and discuss the dependence of the swing period on the initial conditions.By the numerical analysis of the dynamics of the coupled spherical pendulums,we show the influence of the spring stiffness on the energy transfer,discuss the frequency distribution of the energy,and clarify the chaotic state of the nonlinear large swing angle motion.

关 键 词：球面摆 耦合摆 傅里叶变换 非线性运动 

分 类 号：O411.3[理学—理论物理]