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  1. Extension of trigonometric and hyperbolic functions to vectorial arguments and its application to the representation of rotations and Lorentz transformations.H. Yamasaki - 1983 - Foundations of Physics 13 (11):1139-1154.
    The use of the axial vector representing a three-dimensional rotation makes the rotation representation much more compact by extending the trigonometric functions to vectorial arguments. Similarly, the pure Lorentz transformations are compactly treated by generalizing a scalar rapidity to a vector quantity in spatial three-dimensional cases and extending hyperbolic functions to vectorial arguments. A calculation of the Wigner rotation simplified by using the extended functions illustrates the fact that the rapidity vector space obeys hyperbolic geometry. New representations bring a Lorentz-invariant (...)
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