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Periodic problem for the Duffing equation
Asante, Michael Onwona ; Řehák, Pavel (oponent) ; Šremr, Jiří (vedoucí práce)
In the mathematical modelling of physical systems, ordinary differential equations of various forms are used. Differential equations describing these systems are often complex nonlinear equations, however using suitable approximations of nonlinearity, one can derive simple equations called Duffing equations which can be studied analytically. In mathematical modelling of mechanics, the problem of finding periodic solutions to these Duffing equations is closely related to the existence of periodic vibrations of its corresponding nonlinear oscillator. In this work, the analysis of the solutions and existence of solutions in the autonomous and nonautonomous cases of the considered Duffing equation are carried out supported by simulations in MATLAB.
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Periodic solutions to nonautonmous Duffing equation
Zamir, Qazi Hamid ; Řehák, Pavel (oponent) ; Šremr, Jiří (vedoucí práce)
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.
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Periodic problem for the Duffing equation
Asante, Michael Onwona ; Řehák, Pavel (oponent) ; Šremr, Jiří (vedoucí práce)
In the mathematical modelling of physical systems, ordinary differential equations of various forms are used. Differential equations describing these systems are often complex nonlinear equations, however using suitable approximations of nonlinearity, one can derive simple equations called Duffing equations which can be studied analytically. In mathematical modelling of mechanics, the problem of finding periodic solutions to these Duffing equations is closely related to the existence of periodic vibrations of its corresponding nonlinear oscillator. In this work, the analysis of the solutions and existence of solutions in the autonomous and nonautonomous cases of the considered Duffing equation are carried out supported by simulations in MATLAB.
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Periodic solutions to nonautonmous Duffing equation
Zamir, Qazi Hamid ; Řehák, Pavel (oponent) ; Šremr, Jiří (vedoucí práce)
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.
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