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math.OCMay 7, 2007
27
citations (OpenAlex)
authors
  • Yu. L. Sachkov
arXiv abstractPDF
paper

Conjugate points in Euler's elastic problem

arXiv:0705.1003

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.

31 page, 10 figures

References in corpus (1)

  • Maxwell strata in Euler's elastic problem

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  • Cut time in sub-Riemannian problem on Engel group
  • Maxwell strata in sub-Riemannian problem on the group of motions of a plane
  • Left-invariant optimal control problems on Lie groups
  • Exponential mapping in Euler's elastic problem
  • Conjugate points in nilpotent sub-Riemannian problem on the Engel group
  • Conjugate time in sub-Riemannian problem on Cartan group
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