Regular and Chaotic Dynamics

, Volume 20, Issue 6, pp 729–738 | Cite as

On geodesics of the rotation group SO(3)

  • Alyssa Novelia
  • Oliver M. O’Reilly


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.


quaternions constraints geodesics Listing’s law Slerp 

MSC2010 numbers

70E40 53D25 


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA

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