0
$\begingroup$

How to write a two variable function $f(x,t)$ in terms of Dirac-Delta $\delta(x)$ function and a function $P(t)$?

For example;

I read something in a book. You can find the following picture.

But I don' t understand the logic behind this. Could you explain it?

enter image description here

$\endgroup$
0
$\begingroup$

Dirac delta distributions only make sense in an integral. For example, one could want the total work done by the force:

$$W=\int_1^2\boldsymbol{F}\cdot d\boldsymbol{r}$$

In this case, that would mean that all the force is acting on a single point. An integral over a single point gives $0$ ($\int_1^1 = 0$). But since we do want the force to act on the object and do work, we don't want this. In order to have a finite integral value one need to "infinitely concentrate" the force on that point. Thus, the delta dirac distribution.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.