Dirac delta function

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Dirac delta function

[di′rak ′del·tə ‚fəŋk·shən]
(mathematics)
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It has been proved that the inverse operator is the solution of the related equation of the following form, in which the non-homogeneous term has been substituted by the Dirac's delta function [17]:
It should be noted that the Dirac's delta function, because of its rather complex nature, is formally described in terms of the derivative of the Heaviside unit step function [19]:
Diagrams of the Dirac's delta function and Heaviside unit step function are schematically shown in Fig.
Following the method described in [17,20], it is required to solve the following differential equation, by making use of the Dirac's delta function:
It requires the Dirac's delta function to be expanded in the same way, i.
m], however, can be found easily recalling the sifting property of the Dirac's delta function:
Therefore, using Dirac's delta distribution functions, the singular forces must be written as equivalent distributed ones.
n](t) = 0; h(t-[tau]) is the response to Dirac's delta function [delta](t), and is given by