| 复杂非线性电路系统的动力学方程模型 |
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| 引用本文：欧松.复杂非线性电路系统的动力学方程模型[J].计算技术与自动化,2012,(2):7-17 |
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| 中文摘要:Lagrange和Hamilton运动方程是分析力学的基本原理之一和方法论。应用Lagrange和Hamilton原理建立复杂非线性电路保守动力学方程模型是一种形式化可行的方法。对非保守的动力学系统，定义描述电路系统的荷控支路和链控支路的微观结构概念，应用Hamilton结构的方法，可以得到与Lagrange结构等价的方程组；考虑大规模电路系统的复杂性，依据电路系统荷控支路和链控支路微观结构的概念，给出具有控制参量的Lagrange和Hamilton函数，以及具有相应关联矩阵和联接矩阵形式的Lagrange和Hamilton的动态方程；分析了保守和非保守复杂系统拓扑结构关系的描述和其动力学系统的建模，其建模过程具有规范性和方程具有对称性。虽然数学推导过程繁琐，但适合于计算机辅助形式化分析；基于Hamilton方法建立的电路模型为一阶微分动态方程组，特别适合进行理论分析和数值仿真计算。 |
| 中文关键词:Lagrange方程 Hamilton方程 复杂电路系统 保守和非保守系统动力学模型 |
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| The Dynamical Topological Models of Lagrange’s and Hamiltonian Equations for Complex Nonlinear Electrical Circuit System |
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| Abstract:The Lagrange’s and Hamiltonian movement equation are one of the basic principles of analytical mechanics and methodology. The application of Lagrange’s and Hamiltonian theory approach to modeling complex nonlinear conservation electrical circuits dynamics system is a practicable in formulation methodology. But for the non conservation electrical circuits dynamics system, a new micro structure conception of electric charge quantitative control branch and magnetic chain control branch in electrical circuit system has been put forward that have equality with the Lagrange’s equations; Consideration of the topological complexity of large electrical circuit system, based on the micro structure conception of electric charge quantitative control branch and magnetic chain control branch in electrical circuit, and the Lagrange’s and Hamiltonian function that have control parameters are given.; as well as the Lagrange’s and Hamiltonian equations that have incidence matrix and linked matrix; So the complex system topological structure relationship can be specification and find a way out of modeling for this nonlinear conservation and non conservation dynamics model. The modeling processes are formulization and the equations are symmetry. Although the mathematics reduction is complex, but it is appropriate for the formulization supported by computer aided; In addition, the Hamilton methodology models of electrical circuit are first-order differential equation group and this type model is very suitable for theory analysis and numerical simulation. |
| keywords:Lagrange’s equation Hamiltonian equation complex electrical circuit system conservation and non conservation system dynamics model |
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