- #1

James MC

- 174

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I'm trying to comprehend Dirac Delta functions. Here's something to help me understand them; let's say I want to formulate Newton's second law F=MA (for point masses) in DDF form. Is this correct:

[tex] F_i = \int [m_i\delta (x-x_i) a_i\delta (x-x_i)]dx[/tex]

Or is it this:

[tex] F_i = [\int m_i\delta (x-x_i)dx] [\int a_i\delta (x-x_i)dx][/tex]

Or is the idea of a Dirac delta function for the instantaneous acceleration of a point mass not well defined? ...or?

I intially thought the first equation was correct, but then I worried that infinities were being multiplied, and so, I figured that each delta function would need to be integrated first, before the multiplication takes place, hence the second equation.

Any thoughts would be most welcome!