大学物理 ›› 2017, Vol. 36 ›› Issue (2): 20-23.doi: 10.16854 /j.cnki.1000-0712.2017.02.006

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三个耦合摆微幅振动的守恒量与对称性研究

楼智美   

  1. 绍兴文理学院物理系,浙江绍兴312000
  • 收稿日期:2016-02-22 修回日期:2016-06-01 出版日期:2017-02-20 发布日期:2017-02-20
  • 作者简介:楼智美( 1965—) ,女,浙江诸暨人,绍兴文理学院教授,主要从事力学研究与教学工作.
  • 基金资助:
    国家自然科学基金( 11472177) 资助

The study of conserved quantities and symmetries for microvibration of three coupled pendulums

LOU Zhi-mei   

  1. Department of Physics,Shaoxing University,Shaoxing,Zhejiang 312000,China
  • Received:2016-02-22 Revised:2016-06-01 Online:2017-02-20 Published:2017-02-20

摘要: 用拉格朗日方程建立三个耦合摆在微幅振动下的运动微分方程,通过坐标变换实现对拉格朗日函数的解耦,从而直接求得系统的4 个守恒量,并运用Noether 逆定理和Lie 对称性理论分析与守恒量相应的Noether 对称性和Lie 对称性.

关键词: 耦合摆, 守恒量, Noether 对称性, Lie 对称性

Abstract: The kinematic differentiation equations of microvibration of three coupled pendulums are obtained by using Lagrangian equations,we decouple the Lagrangian by transforming coordinates and obtain directly four conserved quantities from uncoupled Lagrangian. The Noether symmetries and Lie symmetries of four conserved quantities are studied by using inverse Noether theorem and Lie symmetry theorem.

Key words: coupled pendulums, conserved quantities, Noether symmetries, Lie symmetries