Can someone expand (curlA.del)(curlA)

I
Thread starter say_cheese
Start date Aug 14, 2017

In summary, "curlA.del" is a mathematical operation that involves taking the dot product of the curl of one vector field with the gradient of another vector field. Expanding "curlA.del" can simplify and provide insights into complex vector calculus expressions, and it is possible for any vector field as long as it is well-defined and differentiable. The expansion process involves applying the product rule and vector calculus identities, and it can be useful in solving practical problems related to fluid dynamics, electromagnetism, and other areas.

Aug 14, 2017

say_cheese

is there a simpler expansion of ((∇xA).∇)(∇xA). This is a common term in fluid equations.

Physics news on Phys.org

Aug 14, 2017

fresh_42

Staff Emeritus

Science Advisor

Insights Author

2023 Award

Please post this question in the homework section and show us your work on it so far. What are ##x## and ##A##? Where are they from? Which do they depend on? What does the point stand for? And simpler than what?

Thread closed.

FAQ: Can someone expand (curlA.del)(curlA)

1. What does "curlA.del" mean in the context of expanding an expression?

"curlA.del" refers to the dot product of the curl of A and the gradient of A. It is a mathematical operation that involves taking the curl of a vector field (A) and then taking the dot product of that result with the gradient of another vector field (A).

2. Why would someone want to expand "curlA.del"?

Expanding "curlA.del" can help simplify and better understand complex vector calculus expressions. It can also provide insights into the relationships between different vector fields and their derivatives.

3. Is it possible to expand "curlA.del" for any vector field?

Yes, it is possible to expand "curlA.del" for any vector field as long as the vector field is well-defined and differentiable. However, the resulting expression may not always be easy to interpret or manipulate.

4. How is "curlA.del" expanded mathematically?

The expansion of "curlA.del" involves applying the product rule and vector calculus identities to the original expression. This can result in a series of partial derivatives and dot products that can then be simplified further.

5. Can expanding "curlA.del" help solve any practical problems?

Yes, expanding "curlA.del" can be useful in solving problems related to fluid dynamics, electromagnetism, and other areas where vector calculus is applicable. It can also aid in visualizing and interpreting physical phenomena described by vector fields.