Coordinate transformations

In summary, the person is seeking help with understanding coordinate transformations while learning about tensors. They are confused about the result they obtained when applying a tensor transformation to a vector in Cartesian coordinates, expecting cylindrical polar components of (r, phi, z) but getting (r, 0, z) instead. They ask for clarification and an explanation of the tensor transformation law being used. The other person suggests that the original conversion may be incorrect as it goes from three variables to two, and provides a different formula for converting from Cartesian to cylindrical coordinates.
  • #1
od7
2
0
Hi.

I’ve just started learning about tensors on my own and am still trying to understand coordinate transformations.

If I begin with a vector whose Cartesian components are (x, y, z) and apply the tensor transformation to cylindrical polars, I end up with (r, 0, z) – is this right? I anticipated (r, phi, z) – have I made an error or am I not understanding something?

Please help!
 
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  • #2
i am not sure what you are doing, but it seems fishy to go from three variables to two. i.e. from a description of three space, to a description of a piece of the plane
 
  • #3
It seems you wish to write a vector [tex] \vec V[/tex]
given in rectangular components
[tex] \vec V= V_x \hat x + V_y \hat y + V_z \hat z[/tex]
in terms of cylindrical polar components
[tex] \vec V=V_r \hat r + V_\phi \hat \phi + V_z \hat z[/tex].
 
  • #4
I am trying to understand the tensor transformation law by applying it directly to a concrete example. If [tex] \vec V=V_x \hat x + V_y \hat \y + V_z \hat z[/tex] then what do I end up with once I have applied the law?
 
  • #5
Could you show the tensor transformation law you are using and the details of your calculation?
 
  • #6
I'm not clear what it is exactly you're trying to do.

If you start out with a vector with compoents in caretsian cooridnates of (x,y,z) the coponents in cylindrical coordinates are (√(x^2 + y^2),arctan(y/x),z)
 

1. What are coordinate transformations?

Coordinate transformations refer to the process of converting one set of coordinates to another. This is often necessary when working with different coordinate systems, such as converting from Cartesian coordinates to polar coordinates.

2. Why are coordinate transformations important in science?

Coordinate transformations are important in science because they allow us to describe and analyze physical phenomena in different coordinate systems. This helps us understand the relationships between different variables and make more accurate predictions.

3. What are some common coordinate systems used in science?

Some common coordinate systems used in science include Cartesian coordinates, polar coordinates, spherical coordinates, and cylindrical coordinates. Each of these systems has its own advantages and is used to describe different types of measurements or phenomena.

4. How are coordinate transformations performed?

Coordinate transformations are performed using mathematical equations or algorithms that relate the coordinates in one system to those in another system. These equations may involve simple calculations or more complex trigonometric functions, depending on the specific transformation being performed.

5. Can coordinate transformations introduce errors in scientific measurements?

Yes, coordinate transformations can introduce errors in scientific measurements if they are not performed accurately. It is important to use the correct equations and ensure that all measurements are converted accurately to avoid introducing errors in the data.

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