双荷子系统运动的经典解

许雪艳; 陈海波; 张宏彬; 丁光涛

doi:10.21656/1000-0887.380046

双荷子系统运动的经典解

doi: 10.21656/1000-0887.380046

¹巢湖学院数理工程研究中心, 合肥 238000;²安徽师范大学物理与电子信息学院, 安徽芜湖 241000

基金项目: 国家自然科学基金（11472063）；高校优秀青年人才支持计划重点项目(gxyqZD2016286)

详细信息

作者简介:
许雪艳（1976—），女，副教授，硕士(通讯作者. E-mail: xuxueyan2002@163.com).

中图分类号: O302;O441
计量
- 文章访问数: 1205
- HTML全文浏览量: 154
- PDF下载量: 514
- 被引次数: 0
出版历程
- 收稿日期: 2017-02-28
- 修回日期: 2017-07-03
- 刊出日期: 2017-09-15

Classical Solutions of Motion for Dyon Systems

¹The Interdisciplinary Center for Study on Maths, Physics and Engineering, Chaohu University, Hefei 238000, P.R.China;²College of Physics and Electronic Information, Anhui Normal University, Wuhu, Anhui 241000, P.R.China

Funds: The National Natural Science Foundation of China（11472063）

摘要

摘要: 根据力学理论和经典电磁理论研究双荷子系统的运动.列出双荷子系统的运动微分方程，导出运动积分，说明系统的对称性，包括SO(4)对称性；利用变分法逆问题方法，构造双荷子系统的Lagrange(拉格朗日)函数和Hamilton(哈密顿)函数；解出双荷子系统的运动规律.
- 双荷子 /
- Lagrange函数 /
- Hamilton函数 /
- 运动积分 /
- 经典电磁理论
Abstract: According to the mechanics theories and the classical electromagnetism, the motion of 2-dyon systems was studied. Some integrals of motion, including the energy integral, the total angular momentum integral and the Runge-Lenz-like integral, were derived from the differential equations of motion for the system, then the SO(4) symmetry of the system was exposed. With the inverse problem method of variational calculus, the Lagrangian function and the Hamiltonian function for the 2-dyon system were constructed. The classical motion of the system is completely integrable, the equations of the orbit and the relation between radial distance r and time t are solvable.
- dyon /
- Lagrangian function /
- Hamiltonian function /
- integral of motion /
- classical electromagnetism

HTML全文

参考文献(16)

[1]	Dirac P A M. Quantised singularities in the electromagnetic field[J]. Proceedings of the Royal Society A: Mathematical Physical & Engineering Sciences,1931,133(821): 60-72.
[2]	Schwinger J. A magnetic model of matter[J]. Science,1969,165(3895): 757-761.
[3]	XU Bo-wei. On SO(4) symmetry of dyons system[J]. Physica Energiae Portis et Physica Nuclearis,1986,10(2): 249-253.
[4]	Ter-Antonyan V M, Nersessian A. Quantum oscillator and a bound system of two dyons[J]. Modern Physics Letters A,1995,10(34): 2633-2638.
[5]	Jackson J D. Classical Electrodynamics [M]. 3rd ed. New York: John & Wiley, 1998.
[6]	WANG Zhong-yue. Generalized momentum equation of quantum mechanics[J]. Optical and Quantum Electronics,2016,48(2): 107.
[7]	Jackson J D, Fox R F. Classical electrodynamics, 3rd ed[J]. American Journal of Physics,1999,67(9): 841.
[8]	Becker M, Caprez A, Batelaan H. On the classical coupling between gravity and electromagnetism[J]. Atoms,2015,3(3): 320-338.
[9]	LI Kang, CHEN Wen-jun, Naón C M. Classical electromagnetic field theory in the presence of magnetic sources[J]. Chinese Physics Letters,2003,20(3): 321-324.
[10]	Santilli R M. Birkhoffian generalization of Hamiltonian mechanics[J]. Journal of Forensic Sciences,1983,54(54):1034-1041.
[11]	Arbab A I. Complex Maxwell’s equations[J]. Chinese Physics B,2013,22(3): 030301-030304.
[12]	Goldstein H, Poole C, Safko J, et al. Classical mechanics, 3rd ed[J]. American Journal of Physics,2002,70(7): 782-783.
[13]	丁光涛. 理论力学[M]. 合肥: 中国科学技术大学出版社, 2013.(DING Guang-tao. Theoretical Mechanics [M]. Hefei: University of Science and Technology of China Press, 2013.(in Chinese))
[14]	Santilli R M. Foundations of Theoretical Mechanics II: Birkhoffian Generalization of Hamiltonian Mechanics [M]. New York: Springer-Verlag, 1982.
[15]	HE Jin-man, XU Yan-li, LUO Shao-kai. Stability for manifolds of the equilibrium state of fractional Birkhoffian systems[J]. Acta Mechanica,2015,226(7): 2135-2146.
[16]	丁光涛. 从第一积分构造Lagrange函数的直接方法[J]. 动力学与控制学报, 2011,9(2): 102-106.(DING Guang-tao. A direct approach to construction of the Lagrangian from the first integral[J]. Journal of Dynamics and Control,2011,9(2): 102-106.(in Chinese))