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 Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 11, Pages 86–91 (Mi ivm7153)

An operator method for studying the Euler problem on types of the loss of stability for a pivoted rod under buckling load

G. G. Sharafutdinova

Chair of Mathematics and Teaching Principles, Sterlitamak State Pedagogical Academy, Sterlitamak, Republic of Bashkortostan, Russia

Abstract: In this paper we propose a new method for defining the Euler critical forces. We construct a scheme that leads to asymptotic formulas defining the bending of a rod both for constant and variable rigidities. The obtained results are based on operator methods of the bifurcation theory.

Keywords: critical forces, bifurcation points, asymptotic formulas, stability, balance state.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:11, 77–82

Bibliographic databases:

UDC: 517.927
Revised: 14.09.2009

Citation: G. G. Sharafutdinova, “An operator method for studying the Euler problem on types of the loss of stability for a pivoted rod under buckling load”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 11, 86–91; Russian Math. (Iz. VUZ), 54:11 (2010), 77–82

Citation in format AMSBIB
\Bibitem{Sha10} \by G.~G.~Sharafutdinova \paper An operator method for studying the Euler problem on types of the loss of stability for a~pivoted rod under buckling load \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2010 \issue 11 \pages 86--91 \mathnet{http://mi.mathnet.ru/ivm7153} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2814567} \transl \jour Russian Math. (Iz. VUZ) \yr 2010 \vol 54 \issue 11 \pages 77--82 \crossref{https://doi.org/10.3103/S1066369X10110083} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649618259}