北京航空航天大学学报 ›› 1999, Vol. 25 ›› Issue (5): 596-600.

• 论文 • 上一篇    下一篇

陀螺仪运动的复杂性

胡志兴, 管克英   

  1. 北京航空航天大学 理学院
  • 收稿日期:1998-04-17 发布日期:2010-11-19
  • 作者简介:男 37岁 博士生 100083 北京
  • 基金资助:

    国家自然科学基金(19671009A),国家教委博士点基金资助项目

Complexity of Motions of Gyroscope

Hu Zhixing, Guan Keying   

  1. Beijing University of Aeronautics and Astronautics, School of Science
  • Received:1998-04-17 Published:2010-11-19

摘要: 建立了外环轴水平放置的重力对称陀螺仪的运动方程.并将陀螺仪转子的质心位置作为扰动, 在一定条件下, 首先研究了自由陀螺仪的运动, 并给出力学意义解释; 然后利用Melnikov方法和KAM理论研究了非自由陀螺仪的运动.研究结果表明: 在陀螺仪转子的质心与支架中心不重合且充分接近, 或陀螺仪能量充分大时, 陀螺仪的运动出现Smale马蹄意义下的混沌; 同时它的Hamiltonian流存在KAM不变环面和不变闭曲线.

Abstract: The motions of a gravity symmetric gyroscope, whose outer ring's axis is placed horizontally, are dealt with. Firstly, the motions of a free gyroscope are studied and explained in the sense of mechanics under a certain condition. The Melnikov's methods and KAM theory can be used to study the motions of a non-free gyroscope if its rotor's gravity center can be treated as a perturbation. It is shown that the motions of the non free gyroscope are chaotic in the sense of Smale horseshoe, and the KAM invariant tori and closed curves exist in the Hamiltonian flows of the perturbed system if the gravity center of the gyroscope's rotor doesn't coincide with the center of its supports, and the distance between them is sufficiently small, or its energy is sufficiently large in comparison with its potential energy.

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