数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 487-494.

• 论文 • 上一篇    下一篇

旋转摆的周期单调性

张军|代冬   

  1. 四川大学数学学院 成都 610064
  • 收稿日期:2012-12-11 修回日期:2013-12-21 出版日期:2014-06-25 发布日期:2014-06-25
  • 基金资助:

    国家自然科学基金 (11221101) 资助

The Period of a Whirling Pendulum

 ZHANG Jun, DAI Dong   

  1. Department of Mathematics, Sichuan University, Chengdu 610064
  • Received:2012-12-11 Revised:2013-12-21 Online:2014-06-25 Published:2014-06-25
  • Supported by:

    国家自然科学基金 (11221101) 资助

摘要:

考虑了一类旋转摆系统.该系统拥有至多5个周期轨族, 通过计算椭圆积分得到了参数在不同取值范围内该系统各个周期轨族的周期单调性. 该文的分析过程也为讨论这类周期单调性问题提供了一个比 Abel积分更基本的方法. 最后给出的数值仿真结果映证了文中的结论.

关键词: 旋转摆, 周期单调性, 椭圆积分

Abstract:

The authors considered a whirling pendulum system. The system has at most five periodic annuli. By calculating the elliptic integrals, The authors obtained the monotonicity of the period of those periodic annuli for various cases of the parameter. The analysis also provides a method to discuss the problem of the monotonicity of period, which is more
fundamental than the one by using Abelian integrals. Finally, the authors given numerical simulations to demonstrate their conclusions.

Key words: Whirling pendulum, Period function, Elliptic integrals

中图分类号: 

  • 34C05