中国物理B ›› 2006, Vol. 15 ›› Issue (5): 891-894.doi: 10.1088/1009-1963/15/5/001

• GENERAL •    下一篇

The Lagrangian and the Lie symmetries of charged particle motion in homogeneous electromagnetic field

楼智美   

  1. Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China
  • 收稿日期:2005-08-04 修回日期:2005-10-16 出版日期:2006-05-20 发布日期:2006-05-20

The Lagrangian and the Lie symmetries of charged particle motion in homogeneous electromagnetic field

Lou Zhi-Mei (楼智美)   

  1. Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China
  • Received:2005-08-04 Revised:2005-10-16 Online:2006-05-20 Published:2006-05-20

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摘要： In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian is also given by means of the obtained constant of motion. By discussing the Lie symmetry for this classical system, this paper obtains the general expression of the conserved quantity. It is shown that the conserved quantity is the same as the constant of motion in essence.

Abstract: In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian is also given by means of the obtained constant of motion. By discussing the Lie symmetry for this classical system, this paper obtains the general expression of the conserved quantity. It is shown that the conserved quantity is the same as the constant of motion in essence.

Key words: constant of motion, Lagrangian, Lie symmetry, conserved quantity

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
45.05.+x (General theory of classical mechanics of discrete systems)