Application research of symplectic Runge-Kutta method of solving Lagrange-Maxwell equation

Liu Shi-Xing; Song Duan; Jia Lin; Liu Chang; Guo Yong-Xin

doi:10.7498/aps.62.034501

Abstract

In this paper, we show the numerical integration method of solving Lagrange-Maxwell equation by using the symplectic Runge-Kutta (R-K) method, and numerically study the motion of the plate in an RLC circuit spring coupled system and the current changes. Its result is consistent with that obtained by the traditional R-K method, which demonstrates symplectic integration algorithm is reasonable and effective in studying the electro-mechanical systems. And on this basis, the form invariance of Noether sense is studied by using the symplectic Runge-Kutta method.

Keywords:

Authors and contacts

1.
College of Physics, Liaoning University, Shenyang 110036, China;
2.
Physics of Medical Imaging Department, Eastern Liaoning University, Dandong 118001, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11172120, 10932002, 10872084), the Research Program of Higher Education of Liaoning Province, China (Grant No. 2008S098), the Program of Supporting Elitists of Higher Education of Liaoning Province, China (Grant No. 2008RC20), and the Program of Constructing Liaoning Provincial Key Laboratory, China (Grant No. 2008403009)

References

[1]	Wen X S, Qiu J, Tao J Y 2003 Analytical Mechanics of Mechanico-electrical Dynamical Systems and its Application (Beijing: Science Press) (in Chinese) [温熙森, 邱静, 陶俊勇 2003 机电系统分析动力学及其应用 (北京: 科学出版社)]
[2]	Qiu J 1992 Analytical Mechanics of Mechanico-electrical Systems (Beijing: Science Press) (in Chinese) [邱家俊 1992 机电分析动力学 (北京: 科学出版社)]
[3]	Zheng S W, Fu J L, Li X H 2005 Acta Phys. Sin. 54 5551 (in Chinese) [郑世旺, 傅景礼, 李显辉 2005 54 5511]
[4]	Fu J L, Chen B Y, Tang Y F, Fu H 2008 Chin. Phys. B 17 3942
[5]	Liu X W, Li Y C 2011 Acta Phys. Sin. 60 111102 (in Chinese) [刘晓巍, 李元成 2011 60 111102]
[6]	Jing-Li Fu, Li-Jun 2004 Chen. Phys. Lett. A 331 138
[7]	Fu J L, Chen L Q, Jiménez S, Tang Y F 2006 Phys. Lett. A 358 2
[8]	Xia L L, Li Y C, Wang X M 2009 Acta Phys. Sin. 58 6732 (in Chinese) [夏丽莉, 李元成, 王小明 2009 58 6732]
[9]	Feng K, Qin M Z 2003 Symplectic Geometric Algorithms for Hamiltonian Systems (Zhejiang: Zhejiang Science & Technology Press) (in Chinese) [冯康, 秦孟兆 2003 哈密尔顿系统的辛几何算法 (浙江: 浙江科学技术出版社)]
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[11]	Lu Y J, Ren G X 2006 Appl. Math. Mech. 27 47 (in Chinese) [路英杰, 任革学 2006 应用数学与力学 27 47]
[12]	Cui Y H, Yang Z A 2006 Journal Vibration and Shock 25 76 (in Chinese) [崔一辉, 杨志安 2006 振动与冲击 25 76]

Cited By

[1]	Wen X S, Qiu J, Tao J Y 2003 Analytical Mechanics of Mechanico-electrical Dynamical Systems and its Application (Beijing: Science Press) (in Chinese) [温熙森, 邱静, 陶俊勇 2003 机电系统分析动力学及其应用 (北京: 科学出版社)]
[2]	Qiu J 1992 Analytical Mechanics of Mechanico-electrical Systems (Beijing: Science Press) (in Chinese) [邱家俊 1992 机电分析动力学 (北京: 科学出版社)]
[3]	Zheng S W, Fu J L, Li X H 2005 Acta Phys. Sin. 54 5551 (in Chinese) [郑世旺, 傅景礼, 李显辉 2005 54 5511]
[4]	Fu J L, Chen B Y, Tang Y F, Fu H 2008 Chin. Phys. B 17 3942
[5]	Liu X W, Li Y C 2011 Acta Phys. Sin. 60 111102 (in Chinese) [刘晓巍, 李元成 2011 60 111102]
[6]	Jing-Li Fu, Li-Jun 2004 Chen. Phys. Lett. A 331 138
[7]	Fu J L, Chen L Q, Jiménez S, Tang Y F 2006 Phys. Lett. A 358 2
[8]	Xia L L, Li Y C, Wang X M 2009 Acta Phys. Sin. 58 6732 (in Chinese) [夏丽莉, 李元成, 王小明 2009 58 6732]
[9]	Feng K, Qin M Z 2003 Symplectic Geometric Algorithms for Hamiltonian Systems (Zhejiang: Zhejiang Science & Technology Press) (in Chinese) [冯康, 秦孟兆 2003 哈密尔顿系统的辛几何算法 (浙江: 浙江科学技术出版社)]
[10]	Liu X S, Ding P Z 2004 Adv. Phys. 26 48 (in Chinesse) [刘学深, 丁培柱 2004 物理学进展 26 48]
[11]	Lu Y J, Ren G X 2006 Appl. Math. Mech. 27 47 (in Chinese) [路英杰, 任革学 2006 应用数学与力学 27 47]
[12]	Cui Y H, Yang Z A 2006 Journal Vibration and Shock 25 76 (in Chinese) [崔一辉, 杨志安 2006 振动与冲击 25 76]

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Catalog

Vol. 62, Issue 3 - 2013-02-05

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