Original title: Periodická řešení neautonomní Duffingovy rovnice
Translated title: Periodic solutions to nonautonmous Duffing equation
Authors: Zamir, Qazi Hamid ; Řehák, Pavel (referee) ; Šremr, Jiří (advisor)
Document type: Master’s theses
Year: 2020
Language: eng
Publisher: Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstract: [eng] [cze]
Ordinary differential equations of various types appear in the mathematical modelling in mechanics. Differential equations obtained are usually rather complicated nonlinear equations. However, using suitable approximations of nonlinearities, one can derive simple equations that are either well known or can be studied analytically. An example of such "approximative" equation is the so-called Duffing equation. Hence, the question on the existence of a periodic solution to the Duffing equation is closely related to the existence of periodic vibrations of the corresponding nonlinear oscillator. Ordinary differential equations of various types appear in the mathematical modeling in mechanics. Differential equations obtained are usually rather complicated nonlinear equations. However, using suitable approximations of nonlinearities, one can derive simple equations that are either well known or can be studied analytically. An example of such "approximative" equation is the so-called Duffing equation. Hence, the question on the existence of a periodic solution to the Duffing equation is closely related to the existence of periodic vibrations of the corresponding nonlinear oscillator.
Keywords: Differential equation; Duffing equation; existence; periodic solution; uniqueness.; Differential equation; Duffing equation; existence; periodic solution; uniqueness.

Institution: Brno University of Technology (web)
Document availability information: Fulltext is available in the Brno University of Technology Digital Library.
Original record: http://hdl.handle.net/11012/195542

Permalink: http://www.nusl.cz/ntk/nusl-579285


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Universities and colleges > Public universities > Brno University of Technology
Academic theses (ETDs) > Master’s theses