辛Runge-Kutta方法在求解Lagrange-Maxwell方程中的应用研究

刘世兴; 宋端; 贾林; 刘畅; 郭永新

doi:10.7498/aps.62.034501

摘要

给出了采用辛Runge-Kutta (R-K)方法求解Lagrange-Maxwell方程的数值积分方法, 并数值研究了RLC电路弹簧耦联系统中极板的运动及电流的变化情况, 其计算结果和传统的R-K方法相一致, 说明利用辛积分算法研究机电动力系统是合理和有效的, 并在此基础上采用辛R-K方法研究了Noether意义下的形式不变性.

关键词:

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:

作者及机构信息

1.
辽宁大学物理学院, 沈阳 110036;

2.
辽东学院影像物理教研室, 丹东 118001

基金项目: 国家自然科学基金(批准号: 11172120, 10932002, 10872084)、辽宁省高校科研基金(批准号: 2008S098)、辽宁省高等学校优秀人才支持计划(批准号: 2008RC20)和辽宁省重点实验室建设项目(批准号: 2008403009)资助的课题.

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)

参考文献

[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 物理学报 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 物理学报 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 物理学报 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]

施引文献

[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 物理学报 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 物理学报 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 物理学报 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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