Conjugate points in Euler's elastic problem
Yu. L. Sachkov
TL;DR
This paper characterizes conjugate points in Euler's elastic problem, showing inflectional elasticae have a conjugate point between the first and third inflection points, while others do not.
Contribution
It provides a detailed description of conjugate points in Euler's elastic problem, clarifying their occurrence in different types of elasticae.
Findings
Inflectional elasticae have a conjugate point between the first and third inflection points.
Non-inflectional elasticae do not have conjugate points.
The paper offers a complete description of conjugate points in the classical problem.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical and Computational Methods · Mathematics and Applications · Advanced Numerical Analysis Techniques