Solution to Euler's elastic problem

DOI10.1134/S0005117909040092zbMath1206.49019OpenAlexW2072896651MaRDI QIDQ1040448

Andrei A. Ardentov, Yuri L. Sachkov

Publication date: 24 November 2009

Published in: Automation and Remote Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0005117909040092

zbMATH Keywords

elastic rodoptimal control problemsystems of algebraic equationsEuler's problem

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Control of mechanical systems (70Q05) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (13)

Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups ⋮ Controlling of a mobile robot with a trailer and its nilpotent approximation ⋮ Relation between Euler's elasticae and sub-Riemannian geodesics on \(\mathrm{SE}(2)\) ⋮ Index theorems for graph-parametrized optimal control problems ⋮ Cuspless Sub-Riemannian Geodesics within the Euclidean Motion Group SE(d) ⋮ Reachable set of the Dubins car with an integral constraint on control ⋮ Conjugate points in nilpotent sub-Riemannian problem on the Engel group ⋮ Unnamed Item ⋮ Association fields via cuspless sub-Riemannian geodesics in SE(2) ⋮ Euler elasticas for optimal control of the motion of mobile wheeled robots: the problem of experimental realization ⋮ Multiple solutions in Euler's elastic problem ⋮ Elastic curves and phase transitions ⋮ A survey of the differential geometry of discrete curves

Uses Software

• Mathematica

Cites Work

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