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.

UDC: 517.927

Received: 25.03.2009
Revised: 14.09.2009

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

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