Conjugate Points in the Euler Elastic Problem

Authors:
Yu. L. Sachkov
Affiliations:
Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Russia 152020
Venue:
Journal of Dynamical and Control Systems
Year:
2008

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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.