Finding the curl in diffrent coordinates by transforming variables

In summary, the conversation discusses transforming an equation for curl in Cartesian coordinates to cylindrical coordinates. The question is whether this transformation can be done and why it may not work. The speaker has attempted to derive the curl using their method but has received an incorrect answer. They suggest posting their attempts for feedback.
  • #1
sentinel
18
0
we have a well known and simple equation for curl in cartesian coo. now we want it in let's say cylindrical coordinates.
question is...can we transform every thing to cylinderical and then use the formula for cartesian?I mean writing basis vectors of cartesian in terms of r and theta and z and basis vectors of cylindrical , and then write the x y z components of the vector(which we want its curl) in terms of its r and theta and z (cylindrical) components and then write the partial differentiations of cartesian in terms of cylindrical r and theta and then write the equation in cartesian>>transform everything to cylindrical>>get the desired formula!
I did this but it gave me wrong answer.WHY??!
I can and did derive the curl in different coordinates by using their definition but using the way I said above it should work...why not?
 
Physics news on Phys.org
  • #2
Hey sentinel and welcome to the forums.

You should note that the basis vectors for the cartesian system are not going to necessarily be the same (length, orientation, etc) in the new system.

Without speculating, you should post what you did here so you can get some specific feedback and suggestions.
 

Related to Finding the curl in diffrent coordinates by transforming variables

What is the concept of finding the curl in different coordinates?

The concept of finding the curl in different coordinates involves transforming the variables of a given vector field to a different coordinate system in order to calculate the curl. This allows for a more efficient and accurate analysis of the vector field in different coordinate systems.

Why is it important to find the curl in different coordinates?

Finding the curl in different coordinates is important because it allows for a better understanding of the behavior of a vector field in different coordinate systems. This can be useful in various scientific and engineering fields, such as fluid dynamics and electromagnetism.

What are the common methods used to find the curl in different coordinates?

The most common methods used to find the curl in different coordinates are the coordinate transformation method and the gradient operator method. The coordinate transformation method involves converting the vector field components to the new coordinate system using transformation matrices, while the gradient operator method uses the gradient of the vector field to calculate the curl.

What are the limitations of finding the curl in different coordinates?

One limitation of finding the curl in different coordinates is that it can be a complex and time-consuming process, especially for more complicated vector fields. Additionally, the accuracy of the results may depend on the chosen coordinate system and the assumptions made during the calculation.

How is finding the curl in different coordinates useful in real-world applications?

Finding the curl in different coordinates has many real-world applications, such as in fluid dynamics, weather forecasting, and structural engineering. It allows for a better understanding and analysis of vector fields in different coordinate systems, which is essential in solving real-world problems and making accurate predictions.

Similar threads

I How to obtain the determinant of the Curl in cylindrical coordinates?
    • Calculus
Replies
3
Views
1K
I Velocity Vector Transformation from Cartesian to Spherical Coordinates
    • Calculus
Replies
2
Views
3K
I A Question about Unit Vectors of Cylindrical Coordinates
    • Calculus
Replies
2
Views
1K
I Is there an algebraic derivation of the area element in polar coordinates?
    • Calculus
Replies
11
Views
2K
A How to find the displacement vector in Spherical coordinate
    • Calculus
Replies
11
Views
5K
I Ampere's Law For Static Magnetic Field
    • Electromagnetism
Replies
5
Views
996
I Curl in cylindrical coordinates
    • Calculus
Replies
4
Views
2K
I Cylindrical coordinates -Curvilinear
    • Differential Equations
Replies
1
Views
414
I Triad T, N, B and path parametrization
    • Calculus
Replies
11
Views
3K
Div and curl in other coordinate systems
    • Calculus
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top