Sagging ropes demonstrate transversality conditions of variational problems

Edward Bormashenko, Gene Whyman, Yelena Bormashenko, Roman Grynyov, Evgeny Shulzinger, Alexander Kazachkov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We present an account of transversality conditions of variational problems and show how they give rise to essential results in the analysis of different physical phenomena. We find such conditions to be a powerful and elegant approach to a diverse number of variational problems with free endpoints. In this work, we illustrate such condition with the study of a heavy inextensible rope sagging both symmetrically and asymmetrically between two variously shaped, steering-guide wires without friction. In such a situation, the transversality conditions lead to the orthogonality of the rope to the wires at endpoints of the rope, which we confirm experimentally. Freeing the endpoints of the rope yields exact analytical equations that predict the tension of the rope. Heavy ropes whose endpoints are free to slip between arbitrarily shaped, steering wires are discussed.

Original languageEnglish
Pages (from-to)998-1002
Number of pages5
JournalAmerican Journal of Physics
Issue number12
StatePublished - 1 Dec 2015


Dive into the research topics of 'Sagging ropes demonstrate transversality conditions of variational problems'. Together they form a unique fingerprint.

Cite this