Switch the divergence coordinate system

In summary, the task is to convert the divergence in Cartesian coordinates to cylindrical coordinates using any method. The student has attempted to use the chain rule but is unsure if they are doing it correctly without seeing their work. They mention derivatives and variables on the left side of the equation.
  • #1
oronanschel
13
0

Homework Statement


i have the divergence in the (x,y,z) Cartesian as [tex]\frac{dA_x}{dx}+\frac{dA_y}{dy}+\frac{dA_z}{dz} [/tex]

and the assignment is to transfer it to cylindrical system [tex](r,{\phi},z)[/tex], by any way i choose.



Homework Equations




tried with the chain rule, but i am doing something wrong, though
i get the gradient in the cylindrical system
 
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  • #2
It is impossible to tell you what, if anything, you are doing wrong if we cannot see what you did!
 
  • #3
look at 1 then 2

then there is 1+2

in the left side there are some derivatives , and variables
transformation to explain


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FAQ: Switch the divergence coordinate system

What is the divergence coordinate system?

The divergence coordinate system is a mathematical framework used to describe the flow of a vector field in three-dimensional space. It is a coordinate system that is based on the divergence of the vector field, rather than the traditional x, y, and z coordinates.

Why is it important to switch the divergence coordinate system?

Switching to the divergence coordinate system can make it easier to analyze and understand the behavior of a vector field. It can also help identify any sources or sinks within the vector field, which can be useful in various scientific and engineering applications.

How do you switch to the divergence coordinate system?

To switch to the divergence coordinate system, you need to calculate the divergence of the vector field and then solve for the new coordinates using a system of partial differential equations. This process can be complex and may require advanced mathematical knowledge.

What are the benefits of using the divergence coordinate system?

Using the divergence coordinate system can simplify the equations used to describe a vector field, making it easier to analyze and interpret the data. It can also help identify any areas of high or low divergence, which can be important in understanding the behavior of the vector field.

Are there any limitations to using the divergence coordinate system?

While the divergence coordinate system can be useful in certain scenarios, it may not be the most appropriate choice for all vector fields. It may also be more difficult to visualize and understand the behavior of the vector field in this coordinate system compared to the traditional x, y, and z coordinates.

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