This article is cited in 23 papers

On Geodesics of the Rotation Group $SO(3)$

Alyssa Novelia, Oliver M. O'Reilly

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1740, USA

Abstract: Geodesics on $SO(3)$ are characterized by constant angular velocity motions and as great circles on a three-sphere. The former interpretation is widely used in optometry and the latter features in the interpolation of rotations in computer graphics. The simplicity of these two disparate interpretations belies the complexity of the corresponding rotations. Using a quaternion representation for a rotation, we present a simple proof of the equivalence of the aforementioned characterizations and a straightforward method to establish features of the corresponding rotations.

Keywords: quaternions, constraints, geodesics, Listing’s law, Slerp.

MSC: 70E40, 53D25

Received: 24.04.2015
Accepted: 25.09.2015

Language: English

DOI: 10.1134/S1560354715060088

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