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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.
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关键词:
- 完整机电系统 /
- 辛R-K方法 /
- Lagrange-Maxwell方程 /
- Noether守恒量
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:
- holonomic electro-mechanical system /
- symplectic Runge-Kutta method /
- Lagrange-Maxwell equation /
- Noether conserved quantity
[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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[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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