摘要
针对第39届全国中学生物理竞赛复赛(延考)第四题,先对四球系统进行受力分析,根据动力学和运动学得到9个(非线性微分)方程,得到两个第一积分(守恒量)。再通过数值模拟给出解答,发现当初始角速度不大时,原参考解答是很好的近似。最后还进一步研究了近似解,得到泰勒展开中精确到t5的结果。整个分析过程为处理力学问题提供了一个参考案例。
For the fourth problem of the 39th National Secondary School Physics Competition Repechage(Extended Examination),the force analysis of the four-ball system is first performed to obtain nine(non-linear differential)equations based on dynamics and kinematics to obtain two first integrals(conserved quantities).The solution is then given by numerical simulation.It is found that the original reference solution is a good approximation when the initial angular velocity is not large.Finally,the approximate solution is further investigated to obtain results accurate to t^5 in the Taylor expansion.The whole analysis provides a reference case for dealing with mechanics problems.
作者
吴洵
姜付锦
何彬
黄亦斌
WU Xun;JIANG Fujin;HE Bin;HUANG Yibin(Poyang Middle School,Shangrao,Jiangxi 333100;Huangpi First Middle School,Wuhan,Hubei 430300;Wanzai Middle School,Yichun,Jiangxi 336000;Jiangxi Normal University,Nanchang,Jiangxi 330022)
出处
《物理与工程》
2023年第5期114-118,共5页
Physics and Engineering
基金
2021年武汉市教育科学规划重点课题《基于新课程标准的高中情境化命题实践研究》阶段性成果之一,课题编号:2021A051。
关键词
刚体动力学
非线性
第一积分
无量纲化
泰勒展开
rigid body dynamics
non-linearity
first integral
dimensionless expansion
Taylor expansion
