The Heaviside Step FunctionDate: 09/03/2003 at 04:40:42 From: Trilochan Subject: Dirac Delta Function I have to calculate the strain energy of a beam, incorporating a term that is zero when the input is below a certain limit, and starts contributing when it reaches that limit. Can I use the Dirac delta function for this? If so, how? If not, is there something else I can use? Date: 09/03/2003 at 15:22:12 From: Doctor Douglas Subject: Re: Dirac Delta Function Hi Trilochan, You might wish to use not the Dirac delta function but rather the Heaviside step function T(x), which is sometimes written with a Greek capital Theta: T(x) = 0 x < 0 = 1 x >= 0 In certain contexts, T(x=0) may be defined to be zero, or perhaps 1/2. The salient feature of this function, however, is that it is zero for negative x, but "turns on" for positive x. You can show that the derivative of T(x) with respect to x is the Dirac delta function. Your equation for the dependence of the strain y upon the stress x might look something like this: y(x) = f(x) + T(x-X)g(x-X), where f and g are functions that you must specify. Note that the second term "turns on" for x >= X. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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