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Given (in spherical coordinates) the resulting 4-vector K of the composition of 2 Lorentz pure rotations R1 and R2, where only R1 is known, I would like to find the angle of the "overall" rotation resulting from this composition.

In other words, I want to find the symbolic expression of the angle of the rotation R when :

R2.R1(U) = R(U) = K

and R2 is a known rotation and K is a known vector (R1, R unknown, U is a vector).

I first thought it would be easy but I have tried several equations and I have also tried to invert some of the rotations to simplify the equation but I should miss some point because I cannot find a reasonable expression (which I know do exist) for this angle.

Any help on that would be highly appreciated!

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# Composition of Lorentz pure rotations

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