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Model of relativistic spinning system
Slezák, Daniel ; Ledvinka, Tomáš (advisor) ; Loukes Gerakopoulos, Georgios (referee)
Contrary to massive point particles, a description of extended bodies dynamics inclu- des higher mass moments, the first of which is spin. In this manner, Mathisson- Papapetrou-Dixon (MPD) equations has to be used instead of the geodesic equation to capture the more complicated evolution of the system. In this work, an extended system is represented by a set of freely moving, occasionally colliding point particles. As an aid in the construction of the model, some of these particles carry negative mass so it is possible to enclose their trajectories by elastic collisions. We then define a system's representative quantities, such as mass, momentum and spin. However, their relativistic theory requires to solve mainly the problems of parallel transport and the choice of a reference frame. Finally - from the known movement of the in- dividual particles, we can show that the whole system obeys the MPD equations. For that we use the simplification of small spacetime curvature along with a more extensive use of parallel transport instead of stress-energy tensor dynamic equation, the significance of which we limit to the behaviour of the component particles.
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Kinematics of particle collisions in the ergosphere of Kerr black hole
Skoupý, Viktor ; Ledvinka, Tomáš (advisor) ; Žofka, Martin (referee)
In the thesis we deal with an effect which can be used to extract energy from a rotating black hole, so-called collisional Penrose process. First we investigate the ways to find the equations of motion in the general relativity using Hamilto- nian. Then we examine the equations of motion and their consequences in several coordinate systems for the space-time in the vicinity of a rotating black hole. Fi- nally we look into ways to create a particle capable to escape to infinity with as big energy as possible using Compton scattering and annihilation. The biggest energy found is approximately 14 times the energy of the incoming particles. The efficiency decreases with the distance from the horizon and with the decreasing specific angular momentum of the black hole. 1
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Solving test-particle equations of motion near a black hole
Ryston, Matěj ; Ledvinka, Tomáš (advisor) ; Suková, Petra (referee)
Bachelor thesis Matěj Ryston 2011/2012 Abstract in English This work aims to give a well-arranged summary of the description and solving the equations of motion of particles outside a black hole (a star) with emphasis on numerical solutions. For that purpose a summary of numerical methods for solving ordinary differential equations, together with a review and comparison of chosen methods, is given. In the second chapter follows a brief recall of the foundations of General Relativity as well as the description of the geometry of Schwarzschild solution of the Einstein equations. After that equations of motion are formulated. In conclusion, selected numerical methods are used on solving said equations of motion of a test particle or those describing bending of light rays in closeness to a black hole.
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Modelling of postcritical states of slender structures
Mašek, Jan ; Eliáš, Jan (referee) ; Frantík, Petr (advisor)
The aim of the presented thesis is to create a compact publication which deals with properties, solution and examination of behavior of dynamical systems as models of mechanical structures. The opening portion of the theoretical part leads the reader through the subject of description of dynamical systems, offers solution methods and investigates solution stability. As the introduction proceeds, possible forms of structure loading, damping and response are presented. Following chapters discuss extensively the possible approaches to system behavior observation and identification of nonlinear and chaotic phenomena. The attention is also paid to displaying methods and color spaces as these are essential for the examination of complex and sensitive systems. The theoretical part of the thesis ends with an introduction to fractal geometry. As the theoretical background is laid down, the thesis proceeds with an application of the knowledge and shows the approach to numerical simulation and study of models of real structures. First, the reader is introduced to the single pendulum model, as the simplest model to exhibit chaotic behavior. The following double pendulum model shows the obstacles of observing systems with more state variables. The models of free rod and cantilever serve as examples of real structure models with many degrees of freedom. These models show even more that a definite or at least sufficiently relevant monitoring of behavior of such deterministic systems is a challenging task which requires sophisticated approach.
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Auto Taxi System Design for Aircraft
Kardoš, Juraj ; Vlk, Jan (referee) ; Chudý, Peter (advisor)
Nedávné studie předpovídají nárůst pasažérů využívajících leteckou dopravu. Tento trend bude vyžadovat zavedení nových leteckých linek, důsledkem čeho bude zhuštěn letový provoz s dopadem hlavně na nápor letišť v metropolitních oblastech. Automatizovaně řízení pojíždení letounu umožní menší rozestupy mezi jednotlivými linkami a zvýšení příletové a odletové kapacity letišť. Tato práce se zabývá návrhem modelu pohybu dopravního letounu po zemi s ohledem na různé provozní podmínky jako např.: stav povrchu vzletové a přistávací dráhy za různého počasí a lišící se provozní parametry letounu (tlak v pneumatikách, zatížení podvozků a pod.). Validace modelu byla založena na sledování poloměru zatáčky pro různe uhly natočení přední podvozkové nohy. Výsledky simulace byly validovany vzhledem k analytickému modelu Ackermanovy geometrie a na specifikační dokument od Boeingu určený pro plánovaní pohybu letounu na letišti. Výsledky prokázaly přesnost modelu a potvrdily jeho možné nasazení pro simulace v reálnem čase.
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Modeling of the Vertical Flight Profile
Valíček, Josef ; Neužil, Tomáš (referee) ; Kučera, Pavel (advisor)
Diplomová práce se zabývá modelováním letadla a simulací různých typů letu. Pro modelování letu bylo podle zadání vybráno proudové letadlo s dlouhým doletem – Gulfstream G550. V první části práce jsou podrobně popsány pohybové rovnice letadla. Dále je vysvětlen numerický model letadla, sestavený na základě pohybových rovnic. Pochopení modelu letadla je nezbytné pro modelování a simulaci vertikálních profilů letu. Práce se zaměřuje na nastavení parametrů modelu letadla podle reálného letadla Gulfstream G550 a modelování vertikálního profilu letu v letové fázi CRUISE. Posledním bodem práce je průzkum optimálního letu letadla vzhledem ke spotřebě paliva. V závěru jsou diskutovány dosažené výsledky a je nastíněn směr případného pokračování práce.
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Utilization of multi-body simulation tools in subject Dynamics
Lokšeninec, Ľuboš ; Houfek, Lubomír (referee) ; Březina, Lukáš (advisor)
The bachelor’s thesis is conducted in purpose of modernization the dynamics theory teaching methods by the multi-body simulation systems. Thesis acquaints student with accessible simulation systems and provides a manual how to compose virtual models of physic frameworks. Student is introduced to the basic options of current multi-body system by means of pre-processed examples focused on rolling, oscillation and inertia moment. Thesis refers to present teaching methods with models composed in Matlab/Simuling system with SimMechanics sublibrary.
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Dynamics of flight and control
Šabartová, Zuzana ; Tomášek, Petr (referee) ; Nechvátal, Luděk (advisor)
This bachelor thesis deals with an analysis of the equations of motion for aircrafts. The equations could be linearized by assuming the steady state flight with small perturbations so that we can use the theory of control. The result of the thesis besides a theoretic aspect is a simulation of motion response due to change of control terms position in MATLAB & Simulink for two particular airplanes.
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Modelling of Free Beam Loaded by Follower Load
Mašek, Jan ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
The aim of the presented thesis is to create a non-linear dynamical model of a free rod loaded by a follower force. The model is inspired by a slender flexible missile loaded by an end thrust. Because of the nature of the problem, the model has to be capable of large deflections. Another requirements on the model are to implement material the damping and the damping due to the interaction of the model with a surrounding medium and the influence of gravitational field. In the future, the model will be used for examination of the post-critical behavior of such construction. Therefore low computational demands of the simulation are required. The derived formulation of the numerical model will be implemented using the Java programming language. For observation of the simulation process and for monitoring of the state variables, an appropriate graphic interface will be created. The accuracy of the derived model will be verified by the comparison of selected values to the analytical solution.
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