均质圆球在回转曲面上的纯滚动运动  

Motion of a homogeneous sphere rolling inside a surface of revolution

作　　者：王睿垠 袁威[2] 冯放[1] 金长江[1] 刘勇[1] WANG Ruiyin;YUAN Wei;FENG Fang;JIN Changjiang;LIU Yong(School of Arts and Sciences,Northeast Agricultural University,Harbin 150030,China;School of Engineering,Northeast Agricultural University,Harbin 150030,China)

机构地区：[1]东北农业大学文理学院,黑龙江哈尔滨150030 [2]东北农业大学工程学院,黑龙江哈尔滨150030

出　　处：《高师理科学刊》2023年第8期57-63,74,共8页Journal of Science of Teachers＇College and University

基　　金：黑龙江省高等教育教学改革项目(SJGY20200065);东北农业大学大北农学者计划基金项目(JYXRRK2019012)。

摘　　要：为了解回转曲面上圆球滚动的运动学和力学特性,以便应用于机器人控制、运动仿真等领域,研究了在回转曲面上纯滚动均匀圆球的运动.对于非完整约束系统,改变切空间坐标框架写出的Euler-Lagrange方程称为Boltzmann-Hamel方程.利用约束特性,采用Boltzmann-Hamel方程,推导出了回转曲面上滚动球体的运动方程.更改运动方程的参数,可以给出滚动球体在圆柱等特殊回转曲面上的运动方程.当回转曲面为圆柱面时,求出了运动方程的解析解.最后通过数值模拟方程的解,给出了均质球在圆柱曲面上的运动轨迹.本文的方程可以适用于任何回转曲面上圆球的纯滚动,为相关工程领域的研究提供理论依据.In order to understand the kinematic and dynamic characteristics of a sphere rolling inside a surface of revolution,and to apply it to fields such as robot control and motion simulation,studied a homogeneous sphere rolling inside a surface of revolution.For nonholonomic constraint systems,Euler-Lagrange equations written in a different coordinate frame is called the Boltzmann-Hamel equations.With the constraint characteristics,uses the Boltzmann-Hamel equations to derive the equations of the sphere rolling inside a surface of revolution.The parameters of the equations can be modified to give the equations of a rolling sphere on special surfaces.When the surface is cylindrical,the analytical solution for the equations has been obtained.Finally,the trajectory of a ball is presented by numerical simulation.The equations presented in this paper can be used for rolling of a sphere on any surface of revolution and provides theoretical support for related engineering fields.

关 键 词：EULER-LAGRANGE方程 Boltzmann-Hamel方程 非完整约束 回转曲面 

分 类 号：O313.3[理学—一般力学与力学基础]