Elastica in SO(3)

T. Popiel, Lyle Noakes

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    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 elastica in Lie groups G equipped with bi-invariant Riemannian metrics, focusing, with a view to applications in engineering and computer graphics, on the group SO(3) of rotations of Euclidean 3-space. For compact G, we show that elastica extend to the whole real line. For G = SO(3), we solve the Euler-Lagrange equation by quadratures.
    Original languageEnglish
    Pages (from-to)105-124
    JournalJournal of the Australian Mathematical Society
    Volume83
    Issue number1
    DOIs
    Publication statusPublished - 2007

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