两自由度带电耦合振子系统的守恒量与近似解

由于两自由度带电耦合振子系统的Lagrange函数中存在耦合项,从而导致其运动微分方程是非线性耦合的.先通过坐标变换消去Lagrange函数中的耦合项,用直接积分法求得系统的守恒量,用Adomian分解法求得系统的近似解,再通过坐标反变换求得系统在原坐标下的守恒量与近似解,并对近似解作了讨论.

Conserved quantities and approximate solutions of a two-dimensional charged coupled oscillator system

Coupled terms are present in the Lagrangian and the corresponding differential equations of a two-dimensional charged oscillator system are nonlinearly coupled. Firstly, the coupled terms in the Lagrangian are eliminated by transformation of coordinates; secondly, the conserved quantities in new coordinates are obtained by direct integral method, and the approximate solutions are obtained by Abdomina decomposition method. Finally, the conserved quantities and the approximate solutions can be expressed in original coordinates by using the inverse transform of the coordinates. The discussion of the approximate solutions is also given in this paper.
Keywords： two-dimensional charged coupled oscillator system conserved quantities approximate sloutions