Conjugate points in Euler's elastic problem

2007/05/07 by Yu. L. Sachkov, Sachkov, Yu. L.
Mathematics · #49J15 #65D07 #74B20 #74K10 #93B29 #93C10 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:49J15 #msc:65D07 #msc:74B20 #msc:74K10 #msc:93B29 #msc:93C10

paper · pdf · doi:10.48550/arxiv.0705.1003

31 page, 10 figures

arxiv created 2007/05/07 · arxiv updated 2009/12/01

Abstract

For the classical Euler's elastic problem, conjugate points are described. Inflectional elasticae admit the first conjugate point between the first and the third inflection points. All the rest elasticae do not have conjugate points.

Related

• Euler's variational approach to the elastica
• Euler's original derivation of elastica equation
• Exponential mapping in Euler's elastic problem
• Relaxed Elastic Line On An Oriented Surface In The Galilean Space
• The critical points of the elastic energy among curves pinned at endpoints