# Oh my delta!

1. Apr 12, 2006

### gulsen

I know $$\Delta W$$, $$dW$$, $$\partial W$$. But what does $$\delta W$$ exactly mean? How does it differ from the previous ones?

2. Apr 12, 2006

### Staff: Mentor

Is that the Dirac delta? Where have you seen the symbol?

3. Apr 12, 2006

### gulsen

Of course it's not Dirac delta.
Classical mechanics book. It's somekind of infintesimal change in work.

4. Apr 12, 2006

### Staff: Mentor

Okay, whatever. What does this classical mechanics book say about it? How is it used differently compared to the first delta symbol in your original question?

5. Apr 12, 2006

### HallsofIvy

Then ask in a physics forum, not mathematics.

6. Apr 12, 2006

### gulsen

It's mathematical operator.
Replace the W with something else if you like. Satisfied?

7. Apr 12, 2006

### Staff: Mentor

Bump...........

8. Apr 12, 2006

### arildno

The VARIATION of a quantity W is very often written as $\delta{W}$

9. Apr 12, 2006

### gulsen

Whoops! Sorry, I didn't notice your post. Really sorry!
That notation pops-up in many places, especially in Lagrangian. I've had a quick look at wikipedia, and found http://en.wikipedia.org/wiki/Lagrangian" [Broken] (at the bottom of the page). I just though this a famous-to-all notation.

I had this somewhere in my after reading https://www.physicsforums.com/showpost.php?p=949279&postcount=15" of Clasius2. I was actually looking for a rigorous definition of it, from the standpoint of a mathematician.

Last edited by a moderator: May 2, 2017
10. Apr 12, 2006

### Integral

Staff Emeritus
That notation falls into the category of symbolism which is defined as you go. Different authors will use it in different ways. It does not have a standard mathematical definition, being a parameter of a physical system which should be defined or clear from context when it is used.

In the link to the Lagrangian you provided it is used to state the "Least action principle". To understand it's meaning you will need to research that term since the author of the article assumes you know about that. So when you understand least action principle then you will understand how it is used in that context.

11. Apr 14, 2006

### dextercioby

It stands for the G^ateaux derivative of the action integral.

Daniel.

12. Apr 14, 2006

### Rach3

It's the differential of a functional.

You have a "functional", a function defined on a space of functions (paths in configuration space). This function assigns to each path, a real scalar, the work associated with that path. Remember with ordinary derivatives, you look at the displacement dy resulting from an infinitesimal dx. There's an analagous concept with functionals, the infinitesimal $\delta W$ associated with an infinitesimal change in path $\,\delta J$ (or whatever notation you use). Look it up in whatever resource you have available on Calculus of Variations.

In this case I do not think it refers to the action integral, that is usually notated by S and the differential $\delta S$.