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Composition of Lorentz pure rotations

  1. Apr 2, 2009 #1
    Hello,

    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!
     
  2. jcsd
  3. Apr 2, 2009 #2
    You actually don't need any reference to the Lorentz group - this is just the normal rotational group SO(3). There are quite some books that cover the parametrization of SO(3). I would suggest to start looking at the represenation of the group SO(3) in terms of so-called Euler angles. (just google it)
     
  4. Apr 2, 2009 #3
    In general the composition of two general boosts will not itself be a boost, but will be a composition of a boost and a spatial rotation.

    The doc

    http://faculty.luther.edu/~macdonal/GAGC/GAGC.html

    under '2.4.4. Composition of boosts' contains a treatment of an algebraic split of such a boost composition into rapidity and rotation angles ... but perhaps somebody else has a reference for you that is free of the clifford algebra used there.
     
  5. Apr 3, 2009 #4

    George Jones

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    By "Lorentz pure rotations" do you mean spatial rotations, as xepma has interpreted, or boosts, as Peeter has interpreted?
     
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