Yu. L. Sachkov, Conjugate points in Euler's elastic problem

Title: Conjugate points in Euler's elastic problem
Authors: Yu. L. Sachkov
Journal title: Journal of Dynamical and Control Systems
Year: 2008
Issue: 3
Volume: 14
Pages: 409 - 439
Abstract:

For the classical Euler elastic problem, conjugate points are described. Inflexional elasticas admit the first conjugate point between the first and third inflexion points. All other elasticas do not have conjugate points. As a result, the problem of stability of Euler elasticas is solved.