Abstract
General m-step rotation sequences are considered in which the kth rotation (k = 1,2,…,m) takes place about an axis whose unit vector is specified with its components in an arbitrary reference frame. A theorem is introduced in order to limit the arbitrariness of these frames so that the overall transformation matrix between the initial and final frames is minimal, i.e. expressible as an m-factor product of only m exponential rotation matrices. Afterwards, expressions are given for the angular velocities associated with such general rotation sequences.
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