Hamilton equations for elasticae in the Euclidean 3-space

DOI10.1016/S0167-2789(00)00040-3zbMath0976.70013OpenAlexW2137952083MaRDI QIDQ1577695

L. M. Pozo Coronado

Publication date: 4 January 2001

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(00)00040-3

zbMATH Keywords

Euler-Lagrange equationsvariational problemHamilton equationsgeneralized symmetrieselasticaefirst-order dynamical systemrigid body motionsspatial curvessquared curvature

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical systems in classical and celestial mechanics (37N05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (3)

Elastica as a dynamical system ⋮ Hamiltonians and conjugate Hamiltonians of some fourth-order nonlinear ODEs ⋮ On Lagrangians and Hamiltonians of some fourth-order nonlinear Kudryashov ODEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The total squared curvature of closed curves
• Poincaré-Cartan forms in higher order variational calculus on fibred manifolds
• Ostrogradski's theorem for higher-order singular Lagrangians
• Elasticae in a Riemannian submanifold
• Exterior differential systems and the calculus of variations
• Elastic curves on the sphere
• The Hamilton-Cartan formalism in the calculus of variations
• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• Parameter-invariant second-order variational problems in one variable
• Existence of free nonclosed Euler–Bernoulli elastica
• The Hamiltonian Theory of Elastica
• Elastic rods, rigid bodies, quaternions and the last quadrature
• Lagrangian Aspects of the Kirchhoff Elastic Rod
• A global formulation of the Lie theory of transformation groups

This page was built for publication: Hamilton equations for elasticae in the Euclidean 3-space