Danail Brezov

Euler Decomposition in a Non-Orthogonal Basis

We obtain covariant expressions for the generalized Euler decomposi-
tion of three-dimensional rotations based on the vector parametriza-
tion construction, proposed by Rodrigues. On the condition that
the axes of rotations in the decomposition form a non-orthogonal ba-
sis, the solution may be written explicitly, with the help of the metric,
in terms of the coordinates of the compound vector parameter in this
basis. These results can be naturally generalized to the case of coplanar
axes, which is the classical Euler decomposition and some specific de-
tails are added concerning the cases of half turns and one-parameter
degenerate solutions (gimbal lock). The problem can also be related to
a coordinate frame, attached to the rotating object as far as physical
applications are concerned.

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		University of Bialystok