Representation of 3D Rotations
In this chapter, we study various aspects of 3D rotations. We first prove Euler’s theorem and show how to parametrize a 3D rotation and how to compute compositions and inverses. For this purpose, we present many different representations of 3D rotations—by a rotation matrix, an angle and an axis, the Euler angles, the Cayley—Klein parameters, and a quaternion. We also discuss topological aspects of SO(3). Finally, we derive invariant measures of SO(3).
KeywordsInvariant Measure Real Root Rotation Matrix Euler Angle Stereographic Projection
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- I. M. Gel’fand, R. A. Minlos, Z. Ya. Shapiro: Representations of the Rotation and Groups and Their Applications (Macmillan, New York 1966)Google Scholar
- T. Brōcker, T. Tom Dieck: Representations of Compact Lie Groups, Graduate Texts in Mathematics, Vol. 98 (Springer, Berlin, Heidelberg 1985)Google Scholar