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IMA Journal of Mathematical Control and Information Advance Access originally published online on November 17, 2005
IMA Journal of Mathematical Control and Information 2006 23(4):463-473; doi:10.1093/imamci/dni069
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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.

Quadratures and cubics in SO(3) and SO(1,2)

Lyle Noakes** and Tomasz Popiel***

School of Mathematics and Statistics, University of Western Australia, Crawley, Western Australia 6009, Australia

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

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

We solve a class of first-order differential equations on SO(3) and SO(1,2) by quadratures. We then consider applications to variational curves, namely, Riemannian cubics, Riemannian cubics in tension, and elastica.

Keywords: Riemannian cubic; Riemannian cubic in tension; elastic curve; elastica; Lax equation; quadrature.

Received on 30 November 2004.


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