Morse theory for elastica

DOI10.3934/jgm.2016006zbMath1352.58003OpenAlexW2416844401MaRDI QIDQ326683

Philip Schrader

Publication date: 12 October 2016

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jgm.2016006

zbMATH Keywords

Palais-Smale conditioncalculus of variationsnonholonomic constraintscurve straighteningEuler-Bernoulli elastica

Mathematics Subject Classification ID

Variational inequalities (49J40) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (3)

GLOBAL ANALYSIS OF ONE-DIMENSIONAL VARIATIONAL PROBLEMS ⋮ Boundary value problems for Euler-Bernoulli planar elastica. A solution construction procedure ⋮ Collision Avoidance of Multiagent Systems on Riemannian Manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The total squared curvature of closed curves
• Curve-straightening in Riemannian manifolds
• Manifolds, tensor analysis, and applications.
• Critical point theory and submanifold geometry
• The Morse index theorem in Hilbert space
• On the geometry of Riemannian cubic polynomials.
• Unified representations of nonlinear splines
• Existence of variationally defined curves with higher order elliptic Lagrangians
• Curve straightening and a minimax argument for closed elastic curves
• Geometry of manifolds of maps
• The influence of elasticity on analysis: The classic heritage
• Elastic circles in 2-spheres
• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• Equilibria of the Curvature Functional and Manifolds of Nonlinear Interpolating Spline Curves
• Curve-straightening and the Palais-Smale condition
• Existence of free nonclosed Euler–Bernoulli elastica
• Non-Euclidean Elastica
• Periodic Geodesics Generator
• Dynamics of relativistic particles with Lagrangians dependent on acceleration
• Finite Dimensional Linear Systems
• Elastica in SO(3)
• Variational Study of Nonlinear Spline Curves
• Condition $\left( {\text{C}} \right)$ and geodesics on Sobolev manifolds
• Integrable Hamiltonian systems on complex Lie groups

This page was built for publication: Morse theory for elastica