Hamilton equations for elasticae in the Euclidean 3-space
type: Item
instance of: scholarly article
title: Hamilton equations for elasticae in the Euclidean 3-space
zbMATH Open document ID: 0976.70013
DOI: 10.1016/S0167-2789(00)00040-3
author: Luis M. Pozo Coronado
published in: Physica D
publication date: 2001-01-04T00:00:00Z
review text: The variational problem of the spatial curves defined by the squared curvature is analyzed by using Hamiltonian formalism. The symmetry of the problem under the rigid body motions is used to reduce the Euler-Lagrange equations to a first-order dynamical system. This allows a qualitative treatment of the problem by using standard dynamical system tools.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 37N05
zbMATH DE Number: 1496074
zbMATH Keywords: Hamilton equations
zbMATH Keywords: elasticae
zbMATH Keywords: generalized symmetries
zbMATH Keywords: variational problem
zbMATH Keywords: spatial curves
zbMATH Keywords: squared curvature
zbMATH Keywords: rigid body motions
zbMATH Keywords: Euler-Lagrange equations
zbMATH Keywords: first-order dynamical system
reviewed by: Teodor Atanacković
MaRDI profile type: Publication
cites work: Q4174811
cites work: Q4692311
cites work: Elastic curves on the sphere
cites work: Reduction for Constrained Variational Problems and � κ 2 2 ds
cites work: Q5731975
cites work: The Hamiltonian Theory of Elastica
cites work: Q4871701
cites work: The Hamilton-Cartan formalism in the calculus of variations
cites work: Exterior differential systems and the calculus of variations
cites work: Q5725219
cites work: Elastic rods, rigid bodies, quaternions and the last quadrature
cites work: Elasticae in a Riemannian submanifold
cites work: The total squared curvature of closed curves
cites work: Lagrangian Aspects of the Kirchhoff Elastic Rod
cites work: Existence of free nonclosed Euler–Bernoulli elastica
cites work: Q3732577
cites work: Poincaré-Cartan forms in higher order variational calculus on fibred manifolds
cites work: Parameter-invariant second-order variational problems in one variable
cites work: Q4849745
cites work: A global formulation of the Lie theory of transformation groups
cites work: Ostrogradski's theorem for higher-order singular Lagrangians
cites work: Q4176177
cites work: Q3290263
full work available at URL: s0167-2789(00)00040-3
OpenAlex ID: W2137952083
description: scientific article; zbMATH DE number 1496074