An excursion into large rotations
Abstract
The matrix formulation of finite rotations in space initiated in Argyris et al (1981) is developed, and it is shown that a consistent but subtle matrix calculus leads directly to several elegant expressions for the transformation or rotation matrix T pertaining to rotation about an arbitrary axis. Attention is also given to the case of multiple rotations about fixed or follower axes, and to an explicit derivation of a single compound rotation vector that is equivalent to two consecutive and arbitrary rotations. Semitangential rotations, for which commutativity holds, are also considered, and an elementary geometrical analysis of large rotations is given. It is believed that the present approach is preferable to a pure vectorial scheme, and is computationally more convenient.
- Publication:
-
Computer Methods in Applied Mechanics and Engineering
- Pub Date:
- September 1982
- DOI:
- 10.1016/0045-7825(82)90069-X
- Bibcode:
- 1982CMAME..32...85A
- Keywords:
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- Axes Of Rotation;
- Matrices (Mathematics);
- Rotation;
- Graphs (Charts);
- Quaternions;
- Transformations (Mathematics);
- Vector Analysis;
- Physics (General)