|
|
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.
|
|
|
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.
|
|
|
Functional analysis and the mathematical pendulum
Čaputa, Daniel ; Šremr, Jiří (referee) ; Řehák, Pavel (advisor)
This thesis is focused on existence of periodic solutions of nonlinear model of mathematical pendulum with continuous, odd and periodic forcing term. In thesis, the differential equation of motion of pendulum is derived and the associated boundary value problem is rewritten as the integral equation. This equation is considered in a wider set of integral equations (Hammerstein equations). Fixed point theorems are applied on these equations what results in existence and uniqueness of solution. These results are applied on model of mathematical pendulum and the condition for uniqueness of solution is deeper discussed.
|
|
|
Functional analysis and the mathematical pendulum
Čaputa, Daniel ; Šremr, Jiří (referee) ; Řehák, Pavel (advisor)
This thesis is focused on existence of periodic solutions of nonlinear model of mathematical pendulum with continuous, odd and periodic forcing term. In thesis, the differential equation of motion of pendulum is derived and the associated boundary value problem is rewritten as the integral equation. This equation is considered in a wider set of integral equations (Hammerstein equations). Fixed point theorems are applied on these equations what results in existence and uniqueness of solution. These results are applied on model of mathematical pendulum and the condition for uniqueness of solution is deeper discussed.
|
|
|
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.
|
|
|
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.
|
|
|
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.
|
guest ::
