LC振荡电路的辛分析法

Symplectic analysis method for LC oscillation circuit

将哈密顿体系辛方法拓展到LC电路,研究LC振荡电路的辛分析法.由以电量q为变量的拉格朗日函数出发,引出对偶变量磁通链ф,将电量q与ф组成状态参量,把LC电路问题导向辛体系.对辛表述下的对偶方程利用分离变量法进行求解,问题转化成了辛本征问题.只要求出系统的哈密顿矩阵H,便可通过求解相应的本征值方程得到LC电路的振荡规律.算例验证了本文方法的有效性和正确性.将LC电路问题导入辛体系,为LC电路提供了一种新的分析方法.

The symplectic method of Hamilton system is discussed and extended to the LC oscillation circuit. By deducing from the Lagrange function with electric quantity q as a variable, the dual variable magnetic linkage φ is educed and the electric quantity q and the magnetic linkage φ are treated as the state parameters. Then the LC circuit problem is directed to a symplectic system. The dual equation can be solved by segregation variable method and it is converted into the symplecticeigen problem. The oscillation law of LC circuit is obtained through the Hamihon matrixH and the corresponding eigenvalue equation. Numerical examples demonstrate the effectiveness and validity of the method proposed in this paper. The LC circuit problem is introduced into the symplectic system, which provides a new analytical method for the LC circuit.