关键词: 哈密顿, 辛, LC 电路

Abstract: 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 is educed and the electric quantity q and the magnetic linkage 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 Hamilton matrix H 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.

Key words: Hamilton, symplectic, LC circuit