I would like to find the original reference in which the polar parameterization of quaternions was given (i.e. the relationship between the components of a unit quaternion and the polar angles of an axis and rotation angle of a three-dimensional rotation). I assume it would have been written by Hamilton, but the physics literature from the 60's doesn't really point back any further (See, e.g. Biedenharn LC. J Math Phys 1961;2:433, equation 10). Any suggestions?
2026-04-02 22:13:08.1775167988
Reference for the polar parameterization of quaternions
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Here is the citation for anyone interested:
W. R. Hamilton, “On a new species of imaginary quantities connected with a theory of quaternions,” Proceedings of the Royal Irish Academy, vol. 2, pp. 424–434, 1844.