Geodesic
An operator method for studying the Euler problem on types of the loss of stability for a~pivoted rod under buckling load
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2010), pp. 86-91.

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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, asymptotic formulas, stability, balance state.
Mots-clés : bifurcation points 
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     author = {G. G. Sharafutdinova},
     title = {An operator method for studying the {Euler} problem on types of the loss of stability for a~pivoted rod under buckling load},
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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. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2010), pp. 86-91. http://geodesic.mathdoc.fr/item/IVM_2010_11_a7/

[1] Yasinskii F. S., Izbrannye raboty po ustoichivosti szhatykh sterzhnei, GITTL, M., 1952

[2] Panovko Ya. G., Gubanova I. I., Ustoichivost i kolebaniya uprugikh sistem: sovremennye kontseptsii, paradoksy i oshibki, Kom-Kniga, M., 2006

[3] Azbelev N. V., Makagonova M. A., Plaksina V. P., “Variatsionnyi metod resheniya zadachi Eilera ob ustoichivosti uprugogo sterzhnya”, Izv. RAEN. Differents. uravneniya, 2004, no. 8, 10–13

[4] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975 | MR

[5] Azbelev N. V., Kultyshev S. Yu., Tsalyuk V. Z., Funktsionalno-differentsialnye uravneniya i variatsionnye zadachi, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva–Izhevsk, 2006 http://www.rcd.ru

[6] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1957 | MR | Zbl

[7] Ibragimova L. S., Yumagulov M. G., “Funktsionalizatsiya parametra i ee prilozheniya v zadache o lokalnykh bifurkatsiyakh dinamicheskikh sistem”, Avtomatika i telemekhanika, 2007, no. 4, 3–12 | MR | Zbl