The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with the product of two deltas as a forcing function. Each problem was solved by an entirely different procedure. In comparison with non-parametric solutions, the present solutions are both more accurate and truer representations of the physics involved.
References
[1]
Chicurel-Uziel, E. (2007) Dirac Delta Representation by Exact Parametric Equations. Application to Impulsive Vibration Systems. Journal of Sound and Vibration, 305, 134-150.
http://dx.doi.org/10.1016/j.jsv.2007.03.087
[2]
Chicurel-Uziel, E. and Godínez-Rojano, F.A. (2013) Parametric Dirac Delta to Simplify the Solution of Linear and Nonlinear Problems with an Impulsive Forcing Function. Journal of Applied Mathematics and Physics, 1, 16-25.
http://dx.doi.org/10.4236/jamp.2013.17003