An Extended Conjugate Point Theory with Application to the Stability of Planar Buckling of an Elastic Rod Subject to a Repulsive Self-Potential

DOI10.1137/080731803zbMath1185.49025OpenAlexW1983382948MaRDI QIDQ3553799

Kathleen A. Hoffman, Robert S. Manning

Publication date: 21 April 2010

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/4280ec49d25e885bb1d208ec11342431aec38a0a

zbMATH Keywords

conjugate points Morse index constrained variational principles nonlocal potential energy

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Control of mechanical systems (70Q05) Optimality conditions for problems involving relations other than differential equations (49K21)

Related Items (9)

Extensibility effects on Euler elastica's stability ⋮ Interacting charged elastic loops on a sphere ⋮ A singularity free approach for Kirchhoff rods having uniformly distributed electrostatic charge ⋮ An improved proof of instability of some Euler elasticas ⋮ On Jacobi's condition for the simplest problem of calculus of variations with mixed boundary conditions ⋮ Dynamic torsional buckling: prebuckling waves and delayed instability ⋮ Jacobi fields in optimal control: Morse and Maslov indices ⋮ A variational rod model with a singular nonlocal potential ⋮ Stability to discontinuous perturbations for one inflexion Euler elasticas with one end fixed and the other clamped in rotation

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