间断和脉冲激励

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Discontinuous and Impulsive Excitation

摘要: 本文讨论由于脉冲和间断激励所引起的含有Dirac函数和Heavisde函数微分方程的求解问题。首先,按照微分方程理论,我们建议把方程解表达为x(t)=x₁(t)+x₂(t)H(t-a);然后,利用广义函数性质,导出x₁(t)和x₂(t)方程,通过求解x₁(t)和x₂(t)来得到原来方程解x(t)。最后,对周期脉冲参数激励问题进行了深入讨论。

Abstract: In this paper,we study the solution of differential equation with Dirac function and Heaviside function,arising from discontinuous and impulsive excitation.Firstly,according to the theory of differential equation,we suggest x(t)=x₁(t)+x₂(t)H(t-a);then we derive the equation of x₁(t) and x₂(t) by terms of property of distribution,and by solving x₁(t) and x₂(t) we obtain x(t);finally,we make a thorough investigation about periodic impulsive parametric excitation.

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