On the necessary and sufficient condition for the decomposition of orthogonal transformations

It is well-known that a generic SO(3) transformation can be decomposed into three consecutive rotations whenever the axis of the second one is perpendicular to the other two [1]. This fact, known as the Davenport condition, provides the maximal generalization to the classical Euler setting. For arbi...

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Bibliographic Details
Format: Conference Proceeding
Language:English
Subjects:
Decomposition
Transformations
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Summary:It is well-known that a generic SO(3) transformation can be decomposed into three consecutive rotations whenever the axis of the second one is perpendicular to the other two [1]. This fact, known as the Davenport condition, provides the maximal generalization to the classical Euler setting. For arbitrary axes, on the other hand, one has a non-trivial decomposability condition [2, 3]. In the present paper we investigate the latter into more detail and use it to derive a simple set of inequalities that specify the range of the compound rotation angle, for which the condition is automatically satisfied. Thus, we obtain an estimate for the minimum number of rotations in a decomposition and provide some numerical examples.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4936733