# Convert cylindrical coordinate displacement to Cartesian

In summary, the user is trying to understand how a solver converts coordinates from cartesian to cylindrical and vice-versa. They have a set of points in cartesian and cylindrical coordinates and are interested in the displacement values in both formats. However, they are only able to get the displacement output in one format and are struggling to understand how the conversion is performed. They are looking for help in understanding how the displacement values in r,theta,z format (0.0060519, -0.0054482, 0.0026499) are converted to x,y,z format (0.0050497, 0.0063882, 0.0026499) and vice-versa.
Summary: I can't figure out how the solver carries out the conversions from cartesian to cylindrical coordinates and vice-versa.

I have a set of points of a finite element mesh which when inputted into a solver (ansys) gives the displacement of each node. I can get the displacement values of each node either in r,theta(in rads),z or x,y,z.
Ex -This is the original coordinates of a node
in cylindrical (r,theta,z) -
0.0480138, 1.634834202, 0.000841226
in Cartesian (x,y,z) -
-0.00307257421, 0.0479153927, 0.000841225971And the displacement values

in cylindrical -
0.0060519, -0.0054482, 0.0026499
in Cartesian -
0.0050497, 0.0063882, 0.0026499

I can only get the displacement output as either in cylindrical or in cartesian format. Right now I'm taking the output in cylindrical format so I need to calculate x,y displacement values. But I can't figure out how the conversion is performed.
So what I want to know is how the displacement in r,theta,z(0.0060519, -0.0054482, 0.0026499) became x,y,z(0.0050497, 0.0063882, 0.0026499) or vice-versa.
Any help will be appreciated.

[Moderator's note: Moved from a technical forum and thus no template.]

Last edited by a moderator:
Those aren't the correct values for x and y:
> r := 0.60519e-2;
theta := -0.54482e-2;
x := r*cos(theta);
y := r*sin(theta);
print(output redirected...); # input placeholder
0.0060519
-0.0054482
0.006051810181
-0.00003297179846

## 1. What is the formula for converting cylindrical coordinate displacement to Cartesian?

The formula for converting cylindrical coordinate displacement to Cartesian is:
x = ρcos(θ)
y = ρsin(θ)
z = z

## 2. What do ρ, θ, and z represent in cylindrical coordinates?

ρ represents the distance from the origin to the point in the xy-plane, θ represents the angle from the positive x-axis to the point in the xy-plane, and z represents the vertical displacement from the xy-plane.

## 3. Can you convert a point from Cartesian coordinates to cylindrical coordinates?

Yes, you can convert a point from Cartesian coordinates to cylindrical coordinates using the formula:
ρ = √(x2 + y2)
θ = tan-1(y/x)
z = z

## 4. How is the cylindrical coordinate system different from the Cartesian coordinate system?

The cylindrical coordinate system uses a distance from the origin and an angle from the positive x-axis to locate a point in the xy-plane, while the Cartesian coordinate system uses the x, y, and z coordinates to locate a point in 3D space.

## 5. Why is it useful to convert between cylindrical and Cartesian coordinates?

Converting between cylindrical and Cartesian coordinates allows us to easily switch between different coordinate systems and solve problems in different contexts. It also makes it easier to visualize and understand the relationship between points in 3D space.

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