Rotating a Vector [x0,y0,z0] in an XYZ Frame

AI Thread Summary
To rotate a vector [x0, y0, z0] in an XYZ frame, specific formulas for each axis are needed. For rotation around the x-axis, the new coordinates are calculated using the formulas y' = y0 * cos(θ) - z0 * sin(θ) and z' = y0 * sin(θ) + z0 * cos(θ). For the y-axis, the transformation yields x' = x0 * cos(θ) + z0 * sin(θ) and z' = -x0 * sin(θ) + z0 * cos(θ). Lastly, for the z-axis, the formulas are x' = x0 * cos(θ) - y0 * sin(θ) and y' = x0 * sin(θ) + y0 * cos(θ). Understanding these transformations can be achieved through basic geometry without relying on matrix operations.
kepler
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Hello,

I've got a vector [x0,y0,z0,] in a xyz frame. What are the formulas to rotate it by the x-axis, the y-axis and the z-axis - separately of course? - Please don't give me matrices operations :bugeye:

Regards,

Kepler
 
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You can develop the transformation yourself with a little geometry by asking how each of the 3 unit vectors gets transformed by each of those rotations. A matrix is simply a way of doing the bookkeeping in a clear way.
 

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