基于Mathematica软件分析受约束多体运动问题  

The Analysis of Constrained Many-body Motion Problem Based on Mathematica

作　　者：郭龙飞 姚宏林 宋铁岭 李柏力 吴昊[1] GUO Longfei;YAO Honglin;SONG Tieling;LI Boli;WU Hao(Department of Basic,Space Engineering University,Beijing 101400)

机构地区：[1]中国人民解放军军事航天部队航天工程大学基础部,北京101400

出　　处：《物理通报》2024年第9期136-139,共4页Physics Bulletin

摘　　要：受约束的多体运动涉及质点运动学、动力学和守恒定律等多方面知识点的综合运用,是大学物理学中比较难的一类问题.本文研究了一个典型的受约束多体运动案例,由两个轻质刚体细杆连接的3个小球.在给定了初始条件后,从守恒定律的角度出发,并给予约束方程,利用Mathematica软件强大的符号运算和解方程能力对此类问题进行求解,得到系统运动的详细过程,包括质点的位置坐标、速度、加速度等物理量随时间的变化,并将其可视化.此外,还讨论了初始条件的改变对运动过程的影响.利用Mathematica软件求解此类问题使学生摆脱繁琐数学的束缚,将更多精力关注在物理知识和概念上的理解,提高学习的效率.Constrained many-body motion involves the comprehensive application of many physical knowledge including particle kinematics,dynamics,conservation law and so on.In this paper,we study a typical case of constrained many-body motion in which three balls are linked by two thin rods with light rigid bodies.If the initial conditions are given,we start from conservation law and constraint equation,using the powerful symbolic operation and equation solving ability of Mathematica software to solve such problems,get the detailed process of the system motion,including the change of position coordinates,velocity and acceleration over time,and visualize it.In addition,we also discuss the effect of the change of initial conditions on the motion process.Using Mathematica software to solve such problems can help students get rid of the shackles of tedious mathematics and pay more attention to the understanding of physics knowledge and concepts,so as to improve the efficiency of learning.

关 键 词：MATHEMATICA 约束 多体运动 

分 类 号：G642[文化科学—高等教育学] O4-4[文化科学—教育学]