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.
Title: Conjugate points in Euler's elastic problem
Authors: Yu. L. Sachkov
Journal title: Journal of Dynamical and Control Systems
Pages: 409 - 439