CLASSIFICATION OF THE SPATIAL EQUILIBRIA OF THE CLAMPED ELASTICA: NUMERICAL CONTINUATION OF THE SOLUTION SET

DOI10.1142/S0218127404009971zbMath1099.74527MaRDI QIDQ4655625

Michael E. Henderson, Sébastien Neukirch

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

Numerical continuationboundary value problem for twisted rodssurface following algorithm

Mathematics Subject Classification ID

Related Items (7)

Writhing instabilities of twisted rods: From infinite to finite length ⋮ Classifications of ideal 3D elastica shapes at equilibrium ⋮ Deformation and vibration of a spatial clamped elastica with noncircular cross section ⋮ A catalogue of stable equilibria of planar extensible or inextensible elastic rods for all possible Dirichlet boundary conditions ⋮ Sufficient Conditions for a Path-Connected Set of Local Solutions to an Optimal Control Problem ⋮ Analytical expression of elastic rods at equilibrium under 3D strong anchoring boundary conditions ⋮ A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling

Cites Work

• Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling
• Classification of the spatial equilibria of the clamped elastica: Symmetries and zoology of solutions
• Helical and localised buckling in twisted rods: A unified analysis of the symmetric case
• Symbolic dynamics of infinite depth: Finding global invariants for BVPs
• MULTIPLE PARAMETER CONTINUATION: COMPUTING IMPLICITLY DEFINED k-MANIFOLDS
• Calculation of the Stability Index in Parameter-Dependent Calculus of Variations Problems: Buckling of a Twisted Elastic Strut
• Numerical Methods for Bifurcations of Dynamical Equilibria
• Hidden symmetry of global solutions in twisted elastic rings
• Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids

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