Elastica in SO(3)

• Autores: Tomasz Popiel, Lyle Noakes
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 83, Nº 1, 2007, págs. 105-124
• Idioma: inglés
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• Resumen

  • 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.