Optimality of Euler's elasticae

DOI10.1134/S106456240706004XzbMath1151.49008OpenAlexW2093002901MaRDI QIDQ957801

Yuri L. Sachkov

Publication date: 1 December 2008

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s106456240706004x

zbMATH Keywords

elastic rodattainable setexistence of optimal controlEuler elasticae

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Existence theories for optimal control problems involving partial differential equations (49J20) Attainable sets, reachability (93B03)

Related Items (4)

Relation between Euler's elasticae and sub-Riemannian geodesics on \(\mathrm{SE}(2)\) ⋮ On stability analyses of three classical buckling problems for the elastic strut ⋮ Solution to Euler's elastic problem ⋮ On the Gamma-convergence of some polygonal curvature functionals

Cites Work

• Nilpotent \((3, 6)\) sub-Riemannian problem
• Control theory from the geometric viewpoint.
• Sub-Riemannian sphere in Martinet flat case
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