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IMA Journal of Mathematical Control and Information Advance Access published online on November 17, 2005
IMA Journal of Mathematical Control and Information, 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.
Received November 30, 2004

Article

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

Lyle Noakes 1 * and Tomasz Popiel 1

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

* To whom correspondence should be addressed.
Lyle Noakes, E-mail: lyle{at}maths.uwa.edu.au


  Abstract

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.
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