Euler-Rodrigues parameters
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In mathematics, Euler-Rodrigues parameters, also called just Euler parameters, are four numbers a, b, c, d such that
- a2+b2+c2+d2=1.
These parameterize the Lie group SU(2) via the expression
.
They are nowadays more commonly called unit quaternions (i.e. quaternions of length 1).
The Euler-Rodrigues formulae express the elements of a 3D rotation matrix in terms of the Euler-Rodrigues parameters.
The Euler-Rodrigues formulae are given in matrix form at SO(4)#The Euler-Rodrigues formula for 3D rotations.
The Euler-Rodrigues parameters and formulae occur in practice in software for artificial satellite altitude control, in software for military flight simulation and in many, if not all computer games.
