Abstract
In a Riemannian manifold M, elastica are solutions of the Euler–Lagrange equation of the following second order constrained variational problem: find a unitspeed 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 biinvariant Riemannian metrics, focusing, with a view to applications in engineering and computer graphics, on the group \operatorname {SO}(3) of rotations of Euclidean 3space. For compact G, we show that elastica extend to the whole real line. For G = \operatorname {SO}(3), we solve the Euler–Lagrange equation by quadratures.
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2000 Mathematics Subject Classification:
primary 49K99, 49Q99

(Metadata: XML, RSS, BibTeX) 
MathSciNet:
MR2354??? 
Z'blattMATH:
1128.49019 
^{†}indicates author for correspondence 
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