力学与实践 ›› 2020, Vol. 42 ›› Issue (4): 526-532.DOI: 10.6052/1000-0879-19-377

• 力学纵横 • 上一篇    下一篇

运用欧拉动力学方程解决力学竞赛两道理论力学试题1)

付靖宇*, 赵增辉*,†,2), 孙伟*   

  1. * 山东科技大学能源与矿业工程学院,山东青岛 266590;
    † 矿业工程国家级实验教学示范中心(山东科技大学),山东青岛 266590;
  • 收稿日期:2019-10-18 出版日期:2020-08-20 发布日期:2020-08-25
  • 通讯作者: 2)赵增辉,副教授,主要从事力学方面的教学与科研工作。E-mail: tgzyzzh@163.com
  • 基金资助:
    1)山东科技大学优秀教学团队建设计划(JXTD20190501)、矿业工程国家级实验教学示范中心开放基金(KYSF20180105)和教育部产学合作协同育人计划(201901273013)资助项目

DISCUSSION ON TWO PROBLEMS OF THEORETICAL MECHANICS IN COLLEGE MECHANICS COMPETITION1)

FU Jingyu*, ZHAO Zenghui*,†,2), SUN Wei*   

  1. * College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590, Shandong, China;
    † National Demonstration Center for Experimental Mining Engineering Education (Shandong University of Science and Technology), Qingdao 266590, Shandong, China
  • Received:2019-10-18 Online:2020-08-20 Published:2020-08-25

摘要: 针对两道力学竞赛试题,从欧拉动力学方程出发分别给出了更加简化的固连系选取方法,分别命名为"Serret-Andoyer近似固连系"和"虚固连系",在此基础上对第1届全国青年力学竞赛理论力学试题第9题,拓展讨论了大球同步旋转时,小球的稳 定性条件,结果表明后者的稳定临界转速要求更低,这将更有利于提高旋转结构的稳定性;对第12届全国周培源大学生力学 竞赛第3题,剖析了任一纬度的运动规律,发现当体系初始角动量为零时会出现一种简洁又优美的运动模式。

关键词: 周培源力学竞赛, 理论力学, 欧拉动力学方程, 科里奥利力, 等效磁矩

Abstract: For two mechanical contest problems, two simplified coordinate systems are used, that is, the "Serret--Andoyer approximate coordinate system" and the "virtual coordinate system" , respectively, based on the Euler dynamics equation. On this basis, the solutions of the stability conditions of the small ball in the synchronous rotation of the big ball in the 9th problem of the 1st national youth mechanics competition are is discussed. The results show that it has lower stability critical speed requirements. This will be more conducive to improving the stability of the rotation structure. For the problem of rotation balls in the 3rd problem of the 12th National Zhou Peiyuan University Mechanics Competition, the universal motion law at any latitude is derived. When the initial angular momentum of the system is zero, a simple and magical motion mode occurs.

Key words: Zhou Peiyuan Mechanics Competition, theoretical mechanics, Euler dynamical equation, Coriolis force, equivalent moment

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