How to make another interpretation of "curl"?

[abcdefg10645]

Recently,I've tried hard to find the physical interpretation of "curl".

But , most of what I found were the same ,that is,"fluid flow"!

I'm now wondering whether there's another annotation so that I can learn more about vecor calculus.

PS.Is there any website which has materials about "vector calculus"?

[abcdefg10645]

Most books I read gave the definition of curl over a vector field \vec{A} is

http://farside.ph.utexas.edu/teaching/em/lectures/node24.html

There came 2 questions:

a. Why we have to take the max in the line integral?

b. Why we have to minimize \Deltas until it approaches to zero ? How to explain it ?

[slider142]

Try Schey's little book "div, grad, curl, and all that" (http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1233418199&sr=8-1). Intuitively, if a vector field is interpreted as a force field, imagine placing a little paddle-wheel in it. The curl tells you relatively how fast your wheel should be spinning due to the vectors pushing in a circular motion about it ("curl" used to be known as "rotation" or "rot(X)" for short). From this, it is obvious that the curl of a constant field is everywhere 0. Also see http://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/ .

[abcdefg10645]

Try Schey's little book "div, grad, curl, and all that" (http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1233418199&sr=8-1). Intuitively, if a vector field is interpreted as a force field, imagine placing a little paddle-wheel in it. The curl tells you relatively how fast your wheel should be spinning due to the vectors pushing in a circular motion about it ("curl" used to be known as "rotation" or "rot(X)" for short). From this, it is obvious that the curl of a constant field is everywhere 0. Also see http://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/ .

Thanks!

After I read the article you post , I can now realize the meaning (or the property) of "curl" more clearly.

:smile:

[Phrak]

I'm now wondering whether there's another annotation so that I can learn more about vecor calculus.

There are other notations, but it's not vector calculus anymore. But I take it, you want more of a feel for it, than more equations.