中国物理B ›› 2007, Vol. 16 ›› Issue (5): 1182-1185.doi: 10.1088/1009-1963/16/5/002

• GENERAL • 上一篇    下一篇

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

楼智美   

  1. Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China
  • 收稿日期:2006-09-23 修回日期:2006-10-23 出版日期:2007-05-20 发布日期:2007-05-20
  • 基金资助:
    Project supported by the Science Research Program from Education Bureau of Zhejiang Province, China (Grant No 20061155).

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

Lou Zhi-Mei(楼智美)†   

  1. Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China
  • Received:2006-09-23 Revised:2006-10-23 Online:2007-05-20 Published:2007-05-20
  • Supported by:
    Project supported by the Science Research Program from Education Bureau of Zhejiang Province, China (Grant No 20061155).

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摘要： In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.

Abstract: In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.

Key words: linear coupled oscillator, conserved quantity, Noether symmetry, Lie symmetry

中图分类号:  (Synchronization; coupled oscillators)

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