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 parameters and formulae occur in practice in software for artificial satellite attitude control, in software for military flight simulation and in many, if not all computer games.
