Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

doi:10.1088/1674-1056/20/3/034502

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 34502-034502.doi: 10.1088/1674-1056/20/3/034502

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇下一篇

Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

张毅

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

收稿日期:2010-09-11 修回日期:2010-10-10 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

Zhang Yi(张毅)^†

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Received:2010-09-11 Revised:2010-10-10 Online:2011-03-15 Published:2011-03-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

摘要/Abstract

摘要： This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.

Abstract: This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.

Key words: symmetry of Hamiltonian, generalized classical mechanics, conserved quantity

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

11.30.Na (Nonlinear and dynamical symmetries (spectrum-generating symmetries)) 02.30.Hq (Ordinary differential equations)

张毅. Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics[J]. 中国物理B, 2011, 20(3): 34502-034502.

Zhang Yi(张毅). Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics[J]. Chin. Phys. B, 2011, 20(3): 34502-034502.

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Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

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