Elastica in SO(3)

DOI10.1017/S1446788700036417zbMath1128.49019MaRDI QIDQ5439909

Tomasz Popiel, Lyle Noakes

Publication date: 30 January 2008

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Riemannian manifoldEuler-Lagrange equationsecond-order constrained variational problems

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Geodesics in global differential geometry (53C22) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items (13)

Left Lie reduction for curves in homogeneous spaces ⋮ Morse theory for elastica ⋮ Extendability of Kirchhoff elastic rods in complete Riemannian manifolds ⋮ Elasticae in Killing submersions ⋮ Finding geodesics joining given points ⋮ Unnamed Item ⋮ Kirchhoff elastic rods in five-dimensional space forms whose centerlines are not helices ⋮ Hyperelastic curves along Riemannian maps ⋮ Bézier Curves in the Space of Images ⋮ QUADRATIC CURVATURE ENERGIES IN THE 2-SPHERE ⋮ Magnetic cubics in Riemannian manifolds associated with different magnetic fields ⋮ GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS ⋮ Finding extremals of Lagrangian actions

Cites Work

• Duality and Riemannian cubics
• Non-null Lie quadratics in E3
• Cubic Splines on Curved Spaces
• LAX CONSTRAINTS IN SEMISIMPLE LIE GROUPS
• Introduction to Classical Integrable Systems
• Non-Euclidean Elastica
• Null cubics and Lie quadratics

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