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How to make another interpretation of curl ?

  1. Jan 31, 2009 #1
    How to make another interpretation of "curl"?

    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"?
  2. jcsd
  3. Jan 31, 2009 #2
    Question about the definition of "curl"

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


    There came 2 questions:

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

    b. Why we have to minimize [tex]\Delta[/tex]s until it approaches to zero ? How to explain it ?
  4. Jan 31, 2009 #3
    Re: How to make another interpretation of "curl"?

    Try Schey's little book "div, grad, curl, and all that". 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/ .
  5. Jan 31, 2009 #4
    Re: How to make another interpretation of "curl"?


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

  6. Jan 31, 2009 #5
    Re: How to make another interpretation of "curl"?

    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.
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