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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 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
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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.
Received: 25.03.2009
Revised: 14.09.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 11, Pages 77–82
DOI: https://doi.org/10.3103/S1066369X10110083
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
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
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\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
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 11
\pages 77--82
\crossref{https://doi.org/10.3103/S1066369X10110083}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649618259}
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