How to Rotate a Vector in Different Coordinate Spaces?

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SUMMARY

The discussion focuses on the challenge of rotating a vector v(r, theta, phi) in different coordinate spaces defined by Euler angles (alpha, beta, gamma) around the x, y, and z axes. The user, Robert, seeks a straightforward method to compute the transformed coordinates r', theta', and phi'. The response suggests using Euler angles as a standard approach, although it acknowledges the complexity involved in the calculations. It is noted that the radial component remains unchanged (r = r').

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ronslow
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I have a vector v(r, theta, phi) in one coordinate space.

I need to calculate the values r', theta' and phi' for the same vector in another coordinate space which is rotated by alpha, beta and gamma about the x, y and z axis respectively
Is there an easy way to do this?

Thanks

Robert
 
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Welcome to PF!

Hi Robert! Welcome to PF! :smile:

(have an alpha: α and a beta: β and a gamma: γ and a theta: θ and a phi: φ :wink:)
ronslow said:
I have a vector v(r, theta, phi) in one coordinate space.

I need to calculate the values r', theta' and phi' for the same vector in another coordinate space which is rotated by alpha, beta and gamma about the x, y and z axis respectively
Is there an easy way to do this?

Not that I know of … except that r =r' :redface:

(you could try http://en.wikipedia.org/wiki/Euler_angles)
 
Euler angles is probably the standard way to do this (I know it's how I was taught) but they're a bit of a pain to do. I recommend switching to a subject that doesn't rotate vectors
 

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