Results 11 to 20 of about 3,067,838 (357)
Constrained Willmore tori and elastic curves in 2-dimensional space forms [PDF]
, 2014 In this paper we consider two special classes of constrained Willmore tori in the 3-sphere. The first class is given by the rotation of closed elastic curves in the upper half plane - viewed as the hyperbolic plane - around the x-axis.
Lynn Heller
semanticscholar +5 more sources
Some minimization problems for planar networks of elastic curves [PDF]
, 2017 In this note we announce some results that will appear in [6] on the minimization of the functional F(Γ) = ∫Γk2 + 1 ds, where Γ is a network of three curves with fixed equal angles at the two junctions.
Anna Dall’Acqua, Alessandra Pluda
semanticscholar +4 more sources
Shape Analysis of Elastic Curves in Euclidean Spaces [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011 This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the IL2 metric, the reparameterization group acts ...
Anuj Srivastava +3 more
semanticscholar +4 more sources
On the elastic closed plane curves [PDF]
Kodai Mathematical Journal, 1985 Studying the variational problem for the functional \(E(C)=(1/2)\int_{C}k^ 2(s)ds\) (C a closed curve, s the arc length parameter of C, k(s) the curvature of C), under the condition \(\int_{C}ds=L=const.\), the author finds the following result: if E(C) is critical for a closed plane curve with \(L=const.\), then the curve C is either the plane circle \
Hiroshi Yanamoto
openalex +3 more sources
Lectures on Elastic Curves and Rods [PDF]
AIP Conference Proceedings, 2008 These five lectures constitute a tutorial on the Euler elastica and the Kirchhoff elastic rod. We consider the classical variational problem in Euclidean space and its generalization to Riemannian manifolds. We describe both the Lagrangian and the Hamiltonian formulation of the rod, with the goal of examining the (Liouville‐Arnol'd) integrability.
D. Singer
semanticscholar +2 more sources
General rigidity principles for stable and minimal elastic curves [PDF]
Journal für die Reine und Angewandte Mathematik, 2023 For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks’ and Sachkov’s rigidity principles for Euler’
Tatsuya Miura, Kensuke Yoshizawa
semanticscholar +1 more source
Constrained elastic curves and surfaces with spherical curvature lines [PDF]
Indiana University Mathematics Journal, 2021 In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be generated by a pair of initial data: a suitable curve of Lie sphere ...
Joseph Cho, M. Pember, Gudrun Szewieczek
semanticscholar +1 more source
Variational analysis of inextensible elastic curves [PDF]
Proceedings of the Royal Society A, 2021 We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers’ method.
G. Bevilacqua, L. Lussardi, A. Marzocchi
semanticscholar +1 more source
Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive ...
Samira Latifi +2 more
doaj +1 more source
Bifurcation of elastic curves with modulated stiffness [PDF]
European journal of applied mathematics, 2020 We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable.
K. Brazda +3 more
semanticscholar +1 more source