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Application of Bessel functions
Lorenczyk, Jiří ; Lomtatidze, Aleksandre (referee) ; Dosoudilová, Monika (advisor)
The purpose of this work is the introduction to the theory of Bessel differential equation and Bessel functions and its application to the problem of the vibration of a circular plate. In order to tackle this problem succesfully, it is needed to find a solution to the Bessel differential equation in the form of the eponymous Bessel functions and it will be shown how to do so. After that, some characteristics of the obtained Bessel functions of the first kind will be thoroughly demonstrated. Then the other solutions to the Bessel differential equation will be introduced, namely Bessel functions of the second kind, Hankel functions and modified Bessel functions which are obtained as a solution to the modified Bessel equation. In the second chapter, the area of interest will be the application of Bessel functions to the problem of the vibration of a circular plate. However, this problem will be severely restricted since the board will be considered to be perfectly fixed around its circumference, there will be no holes in it and there will be no external force acting on its surface. To solve this problem, it will be needed to make a use of each of the aformentioned Bessel functions.
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Mathematical description of vehicle motion trajectory
Lorenczyk, Jiří ; Popela, Pavel (referee) ; Porteš, Petr (advisor)
The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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Mathematical description of vehicle motion trajectory
Lorenczyk, Jiří ; Popela, Pavel (referee) ; Porteš, Petr (advisor)
The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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|
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Application of Bessel functions
Lorenczyk, Jiří ; Lomtatidze, Aleksandre (referee) ; Dosoudilová, Monika (advisor)
The purpose of this work is the introduction to the theory of Bessel differential equation and Bessel functions and its application to the problem of the vibration of a circular plate. In order to tackle this problem succesfully, it is needed to find a solution to the Bessel differential equation in the form of the eponymous Bessel functions and it will be shown how to do so. After that, some characteristics of the obtained Bessel functions of the first kind will be thoroughly demonstrated. Then the other solutions to the Bessel differential equation will be introduced, namely Bessel functions of the second kind, Hankel functions and modified Bessel functions which are obtained as a solution to the modified Bessel equation. In the second chapter, the area of interest will be the application of Bessel functions to the problem of the vibration of a circular plate. However, this problem will be severely restricted since the board will be considered to be perfectly fixed around its circumference, there will be no holes in it and there will be no external force acting on its surface. To solve this problem, it will be needed to make a use of each of the aformentioned Bessel functions.
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