光滑圆筒中的四球问题——对39届中学生物理竞赛复赛(延考)第四题的思考  

FOUR-BALL PROBLEM IN A SMOOTH CYLINDER——REFLECTIONS ON QUESTION 4 OF THE 39TH SECONDARY SCHOOL STUDENTS'PHYSICS COMPETITION REMATCH(EXTENDED EXAMINATION)

作　　者：吴洵 姜付锦[2] 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)

机构地区：[1]江西省鄱阳中学,江西上饶333100 [2]湖北省武汉市黄陂一中,湖北武汉430300 [3]江西省万载中学,江西宜春336000 [4]江西师范大学,江西南昌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。

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.

关 键 词：刚体动力学 非线性 第一积分 无量纲化 泰勒展开 

分 类 号：G634.7[文化科学—教育学]