求解电感电路的传递辛矩阵方法THE METHOD OF THE TRANSFERSYMPLECTIC MATRIX TO SOLVE INDUCTANCE CIRCUIT
杨红卫,高冉冉,孟珊珊
摘要(Abstract):
本文将电感电路问题导向辛体系,探讨电感电路的辛分析方法。以电感一端的电势及通过电感的电流变化率作为状态参量,通过对简单电感电路、串联电感电路以及复杂电感电路进行分析,给出了电感电路的传递辛矩阵解法。该方法只需求出状态间的辛传递矩阵,再结合边界条件便可对问题进行求解,为电感电路提供了一种新的分析途径。算例验证了本文方法的有效性和正确性。该方法仅涉及简单的矩阵代数运算,易于理解,便于编程。
关键词(KeyWords): 电感;电路;辛;传递矩阵
基金项目(Foundation): 国家自然科学基金(批准号:11172008)资助
作者(Author): 杨红卫,高冉冉,孟珊珊
参考文献(References):
- [1]Weyl H.The Classical Groups,Their Invariants and Representations[M].New Jersey:Princeton University Press,1939.
- [2]冯康,秦孟兆.哈密顿系统的辛几何算法[M].杭州:浙江科学技术出版社,2003.Feng K,Qin M Z.Symplectic Geometric Algorithms for Hamiltonian Systems[M].Hangzhou:Zhejiang Science and Technology Publishing House,2003.(in Chinese)
- [3]钟万勰.应用力学的辛数学方法[M].北京:高等教育出版社,2006.Zhong W X.Symplectic Solution Methodology in Applied Mechanics[M].Beijing:Higher Education Press,2006.(in Chinese)
- [4]钟万勰.电磁波导的辛体系[J].大连理工大学学报,2001,41(4):379-387.Zhong W X.Symplectic system of electro-magnetic waveguide[J].Journal of Dalian University of Technology,2001,41(4):379-387.(in Chinese)
- [5]杨红卫.求解电容电路的辛传递矩阵法[J].电气电子教学学报,2009,31(2):37-39.Yang H Y.The Method of the Transferring Matrix to Solve Capacitor Circuits[J].Journal of Electrical and Electronic Education,2009,31(2):37-39.(in Chinese)
- [6]杨红卫,孟珊珊,王改页,等.求解电阻电路的传递辛矩阵方法[J].物理与工程,2015,25(6):37-40.Yang H W,Meng S S,Wang G Y,et al.Method of Solving the Transfer Symplectic Matrix in Resistance Circuit[J].Physics and Engineering,2015,25(6):37-40.(in Chinese)
- [7]徐新生,周震寰.二维稳态热传导问题中的辛方法[J].热科学与技术,2006,5(4):288-294.Xu X S,Zhou Z H.Symplectic Method in Two Dimensional Thermal Conductionunder Steady State[J].Journal of Thermal Science and Technology,2006,5(4):288-294.(in Chinese)
- [8]钟万勰.力、功、能量与辛数学[M].大连:大连理工大学出版社,2007.Zhong W X.Force,Work,Energy and Symplectic Mathematics[M].Dalian:Dalian University of Technology Press,2007.(in Chinese)
- [9]王勇,龙建忠,方勇,等.电路理论基础[M].北京:科学出版社,2005.Wang Y,Long J Z,Fang Y,et al.Fundamental of Electrical Circuit Theory[M].Beijing:Science Press,2005.(in Chinese)