• 力学纵横 •

### 运用欧拉动力学方程解决力学竞赛两道理论力学试题1)

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

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.