On the use of quaternions in spherical and positional astronomy

Astronomy and Astrophysics – Astronomy

Scientific paper

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Astrometry, Quaternions, Floating Point Arithmetic, Rotating Environments, Trigonometry

Scientific paper

Quaternions can be used advantageously in order to describe rotations in three-dimensional space without having to resort to the juxtaposition of three Eulerian rotations for this movement. As half-angle arguments enter into the formulation of the quaternions, a method is at hand to derive systematically all half-angle formulas of spherical trigonometry. This is achieved in two alternative ways which transfer a tangent vector from one side of the spherical triangle to the opposite vertex. Supplementary to all the half-angle formulas, a set of 12 additional half-angle formulas is derived.

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