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IMA Journal of Mathematical Control and Information Advance Access originally published online on July 28, 2005
IMA Journal of Mathematical Control and Information 2005 22(4):477-488; doi:10.1093/imamci/dni040
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Null Riemannian cubics in tension in SO(3)

Lyle Noakes** and Tomasz Popiel***

School of Mathematics and Statistics, University of Western Australia, Nedlands, WA 6009, Australia

** Email: lyle{at}maths.uwa.edu.au

*** Email: popiet01{at}maths.uwa.edu.au

Riemannian cubics in tension in the rotation group SO(3) are variational curves with applications to interpolation problems in computer graphics and rigid-body trajectory planning. They are related by a linking equation to Lie quadratics in tension (LQT) in the Lie algebra so(3). This paper provides a qualitative analysis of the null case of LQT in so(3).

Keywords: Lie group; Lie algebra; Riemannian cubic in tension; Lie quadratic; curvature; torsion; asymptotics; axes.

Received on 7 July 2004. revised on 10 December 2004. accepted on 13 December 2004.


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