偏心椭球体回转平衡及其稳定性的研究  

MOTION OF THE ECCENTRIC ELLIPSOID: GYROSCOPIC BALANCE CONDITION AND STABILITY

作　　者：李露仙 朱攀丞 李晋斌[1,3] LI Luxian;ZHU Pancheng;LI Jinbin(College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;Key Laboratory of Intelligent Nano Materials and Devices of Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

机构地区：[1]南京航空航天大学理学院,南京210016 [2]南京航空航天大学航空宇航学院,南京210016 [3]南京航空航天大学纳智能材料器件教育部重点实验室,南京210016

出　　处：《力学与实践》2018年第1期56-60,66,共6页Mechanics in Engineering

基　　金：南京航空航天大学教改项目(2017JG08335)资助

摘　　要：本文研究了摩擦系数和偏心距离对偏心椭球体回转平衡的影响,得到了椭球极轴与地面法向夹角的运动方程,导出了两类稳定解.结果表明摩擦力是椭球能否旋转至直立的必要条件,当偏心距一定,摩擦系数越大其运动至直立所需的时间越短.偏心距阻碍直立现象的出现,摩擦系数一定,偏心距越大,其运动至直立所需的时间越长.当偏心距值增大到一定程度,其将无法直立而是至一稳定的角度,并且稳定角度正比于偏心距,偏心距继续增大,将不会出现回转平衡.This paper studies the influence of the friction coe±cient1and the eccentric distance p on the gyroscopic balance in the rotating process of the eccentric ellipsoid.The time evolution of the angleθ=θ(t)and two kinds of stationary solutions are obtained.Our numerical results show that the frictional force is an essential condition for spinning vertically,and can enhance it.That is,when p is constant,the time requiredfor the ellipsoid to standing upright decreases with the increase of1.The eccentric distance will delay the process of the standing upright of the rotator,and with the increase ofμ,for a given frictional coefficientμ,it takes more time to reach the gyroscopic balance.When p keeps increasing,the ellipsoid will eventually take a position of a stabilized angleμf rather than an upright one,andμf is proportional to p.The equivalent section curves are obtained corresponding to these values of eccentricity.When p continues to increase,a point will be reached where there will be no gyroscopic balance anymore.

关 键 词：偏心椭球 摩擦系数 偏心距离 稳定角度 

分 类 号：O318.2[理学—一般力学与力学基础]