Elastica in SO(3)

Tomasz Popiel, Lyle Noakes

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)


In a Riemannian manifold M, elastica are solutions of the Euler-Lagrange equation of the following second order constrained variational problem: find a unit-speed curve in M, interpolating two given points with given initial and final (unit) velocities, of minimal average squared geodesic curvature. We study elástica in Lie groups G equipped wim bi-invariant Riemannian metrics, focusing, with a view to applications in engineering and computer graphics, on the group 50(3) of rotations of Euclidean 3-space. For compact G, we show that elástica extend to the whole real line. For G = 50(3), we solve the Euler-Lagrange equation by quadratures.

Original languageEnglish
Pages (from-to)105-124
Number of pages20
JournalJournal of the Australian Mathematical Society
Issue number1
Publication statusPublished - Aug 2007
Externally publishedYes

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