How to make another interpretation of curl ?

In summary, the conversation discusses the physical interpretation of "curl" and the different resources available for learning about vector calculus. The concept of "curl" is explained as representing the circular motion of vectors in a force field, and it is suggested to read Schey's book "div, grad, curl, and all that" for a better understanding.
  • #1
abcdefg10645
43
0
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"?
 
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  • #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

http://farside.ph.utexas.edu/teaching/em/lectures/node24.html" [Broken]

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 ?
 
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  • #3


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/ .
 
  • #4


slider142 said:
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/ .

Thanks!

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

:smile:
 
  • #5


abcdefg10645 said:
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.
 

1. What is curl and why is it important in science?

Curl is a mathematical concept that describes the rotation or circulation of a vector field. It is important in science because it is used to understand fluid flow, electromagnetism, and other physical phenomena.

2. How is curl different from divergence?

Curl and divergence are both mathematical operations that are used to describe vector fields. The main difference is that curl describes the rotation of a vector field while divergence describes the expansion or contraction of a vector field.

3. What are the different interpretations of curl?

There are several interpretations of curl, including the circulation interpretation, the vorticity interpretation, and the solenoidal interpretation. Each interpretation helps to understand a different aspect of curl.

4. How can curl be calculated?

Curl can be calculated using a mathematical formula that involves taking the partial derivatives of the vector field with respect to each coordinate. Alternatively, it can also be calculated using vector calculus operations such as the cross product.

5. How can curl be applied in real-world scenarios?

Curl has many practical applications in fields such as fluid mechanics, electromagnetism, and weather forecasting. It is used to understand and model the behavior of fluids and electromagnetic fields, and can also be used to analyze and predict the movement of air masses in weather patterns.

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