Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 487-494.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 34C05
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