电动力学中衰减机械系统的非线性振荡方法

衰减机械系统的非线性振荡可用来研究长约瑟夫逊结的电动力学方程式，而这方程式等同于弱衰减机械系统的非线性振荡。本文应用的方法是将控制方程线性化及结合谐波平衡法（线性谐波平衡法）而产生色散关系，再把平均法应用在弱非线性的耗散系统中得到非常准确的瞬变反应。在此提出的方法不仅考虑能量耗散，而且利用简单的线性代数等式关系来代替冗长及复杂的分析近似解。

Damped Mechanical System Nonlinear Oscillation Approach in Electrodynamics

The nonlinear oscillation of damped mechanical systems is applied to investigate the electrodynamics of long Josephson junction. The latter has been shown as equivalent to the weakly damped mechanical nonlinear oscillation system. This paper applies the combination of linearized governing equation and harmonic balancing method (LHBM) to yield the dispersion relation. The application of the method of averaging is then employed to achieve very accurate transient responses of the weekly dissipative system. The proposed approach herein not only accounts for energy dissipation but also presents the relationship of simple linear algebraic equations instead of lengthy and complicated analytical approximate solutions.