Discontinuous and impulsive excitation (Q1087346)

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) \(=\) \(x_ 1(t)\) \(+\) \(x_ 2(t)H(t-\alpha)\); then we derive the equation of \(x_ 1(t)\) and \(x_ 2(t)\) by terms of property of distribution, and by solving \(x_ 1(t)\) and \(x_ 2(t)\) we obtain x(t); finally, we make a thorough investigation about periodic impulsive parametric excitation.