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Mathematical pendulum
Kučerová, Barbora ; Dub, Petr (referee) ; Franců, Jan (advisor)
This bachelor’s thesis deals with the mathematical modeling of the behaviour of mathematical pendulum. The aim of this thesis is to find the equation of mathematical pendulum, compute the trajectories of solution and interpret their meaning, clasify the singular solution, plot the phase portrait in MATLAB software for the basic model and for the generalized model of the damped and driven pendulum.
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Planar dynamics of the mathematical pendulum
Rauš, Michal ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is focused on the mathematical modeling of a motion of simple and double pendulum with the use of an ordinary differential equations. It's main objectives are a derivation of equations of motion, an assessment of stability as well as periodic behaviour of respective models and graphical interpretation of achieved results.
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Periodic solutions to differential equations in modelling of motion of mechanical systems
Koukalová, Kateřina ; Nechvátal, Luděk (referee) ; Šremr, Jiří (advisor)
This thesis focuses on modelling the motion of mechanical systems using differential equations. The mechanical system is represented by a charged pendulum attracted by two charged particles. The thesis deals with the analysis of the differential equation describing the motion of the pendulum, in particular the singular points of the studied equation. We determine their number, type and stability. Based on the values of the parameters of the mechanical system, the singular points differ, phase portraits are drawn for each case.
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Planar dynamics of the mathematical pendulum
Rauš, Michal ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is focused on the mathematical modeling of a motion of simple and double pendulum with the use of an ordinary differential equations. It's main objectives are a derivation of equations of motion, an assessment of stability as well as periodic behaviour of respective models and graphical interpretation of achieved results.
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Mathematical pendulum
Kučerová, Barbora ; Dub, Petr (referee) ; Franců, Jan (advisor)
This bachelor’s thesis deals with the mathematical modeling of the behaviour of mathematical pendulum. The aim of this thesis is to find the equation of mathematical pendulum, compute the trajectories of solution and interpret their meaning, clasify the singular solution, plot the phase portrait in MATLAB software for the basic model and for the generalized model of the damped and driven pendulum.
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Periodic solutions of damped oscillations
HOLUB, Miroslav
The main topic of the Thesis is qualitative analysis of linear differential equations of second order. The Thesis is divided into five parts. At the first part there are explained basic type of oscillators (mathematical pendulum and spring). The second part is devoted to definitions and theorems, which are necessary in the study of differential equations. The third part shows the model of linear differential equation of second order. The solution of this equation depending on various parameters is indicated in the fourth part. Some open questions are formulated in the last part.
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