阻尼振荡的数学本质分析

Mathematical Essence Analyses of Damped Oscillation

用微分方程定性理论,从平面自治系统奇点的性态角度出发分析了阻尼振荡的数学本质.以全新的视角讨论了三种阻尼情况的本质区别,由此引出了系统在平衡态的稳定性问题.进一步用系统稳定性理论论述了自激振荡器的设计思想.该分析方法也是研究非线性动态电路、动力系统稳定性的有效方法.

The mathematical essence of damped oscillation is researched with the qualitative theory of differential equation from the odd characters of the plane autonomous system. Three kinds of damped conditions are discussed with new angle of view, and then problems of system stability are leaded and the principle of self - sustained oscillation is stated. It is an effective way to analyze the stability of nonlinear circuit and dynamic system.