RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 4 scientific papers (total in 4 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

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

References: PDF file   HTML file

Bibliographic databases:

MSC: 70E40, 53D25
Received: 24.04.2015
Accepted:25.09.2015
Language:

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}


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

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  crossref  mathscinet  isi  scopus
    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.  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi  scopus
    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.  crossref  isi
  • Number of views:
    This page:72
    References:13

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019