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 Regul. Chaotic Dyn., 2015, Volume 20, Issue 6, Pages 729–738 (Mi rcd41)

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

DOI: https://doi.org/10.1134/S1560354715060088

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Bibliographic databases:

MSC: 70E40, 53D25
Accepted:25.09.2015
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Citation: Alyssa Novelia, Oliver M. O'Reilly, “On Geodesics of the Rotation Group $SO(3)$”, Regul. Chaotic Dyn., 20:6 (2015), 729–738

Citation in format AMSBIB
\Bibitem{NovOre15} \by Alyssa Novelia, Oliver M. O'Reilly \paper On Geodesics of the Rotation Group $SO(3)$ \jour Regul. Chaotic Dyn. \yr 2015 \vol 20 \issue 6 \pages 729--738 \mathnet{http://mi.mathnet.ru/rcd41} \crossref{https://doi.org/10.1134/S1560354715060088} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431187} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..729N} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000365809000008} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948989680} 

• http://mi.mathnet.ru/eng/rcd41
• http://mi.mathnet.ru/eng/rcd/v20/i6/p729

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. Fischle, P. Neff, “The geometrically nonlinear Cosserat micropolar shear-stretch energy. Part II: Non-classical energy-minimizing microrotations in 3D and their computational validation”, ZAMM-Z. Angew. Math. Mech., 97:7 (2017), 843–871
2. O. O'Reilly, Modeling Nonlinear Problems in the Mechanics of Strings and Rods. The Role of the Balance Laws, Interaction of Mechanics and Mathematics, Springler, 2017, 425 pp.
3. E. G. Hemingway, O. M. O'Reilly, “Perspectives on Euler angle singularities, gimbal lock, and the orthogonality of applied forces and applied moments”, Multibody Syst. Dyn., 44:1 (2018), 31–56
4. M. K. Jawed, A. Novelia, O. M. Reilly, A primer on the kinematics of discrete elastic rods, SpringerBriefs in Thermal Engineering and Applied Science, Springer, 2018, xiii+118 pp.