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Mathematical models of military conflicts
Skopal, Martin ; Potůček, Radovan (referee) ; Čermák, Jan (advisor)
This thesis discusses the mathematical models used in the theory of warfare. The aim is to build and describe the Richardson model of conict and selected Lanchester models of combat. The models are subsequently analysed with a focus on stability. A part of the thesis is also formed by application of real data onto the models and by the subsequent evaluation of their results.
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Real Time Dynamic System Control
Adamík, Pavel ; Kaluža, Vlastimil (referee) ; Kunovský, Jiří (advisor)
This thesis focuses on the methodology of controlling dynamic systems in real time. It contents a review of the control theory basis and the elementary base of regulators construction. Then the list of matemathic formulaes follows as well as the math basis for the system simulations using a difeerential count and the problem of difeerential equations solving. Furthermore, there is a systematic approach to the design of general regulator enclosed, using modern simulation techniques. After the results confirmation in the Matlab system, the problematics of transport delay & quantization modelling follow.
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REINFORCED CONCRETE CYLINDRICAL TANK
Chumová, Petra ; Podroužková, Božena (referee) ; Šulák, Pavel (advisor)
The Bachelor´s thesis focuses on a static solution of reinforced concrete cylindrical tank. The thesis comprises dimensioning of the bottom of the tank and its walls to selected load cases and processing a drawing documentation. The calculation of internal forces is done using the software Scia Engineer. The validation of results is performed by hand calculation using differential equations on a simplified model for the results of internal forces in the wall of the tank.
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Differential equations in models of motion of dislocations
Vydrová, Jana ; Řehák, Pavel (referee) ; Šremr, Jiří (advisor)
This thesis deals with the differential equation which appears in the mathematical model by thermally activated motion of dislocations. It’s focused on screw dislocations in bodycentred cubic metals. Especially solves derivation of the pertinent differential equaiton and then explores properties of their solutions. To research these properties are used knowledges and techniques of qualitative theory of differential equations.
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The Importance of Laplace Transform in Regulation Theory
Kovářová, Karolína ; Dobrovský, Ladislav (referee) ; Dosoudilová, Monika (advisor)
This bachelor's thesis deals with the significant role of Laplace transform in regulation theory. The theoretical part is dedicated to the properties of this integral transform and the description of the control system. The usage of Laplace transform in search of process variable, step and impulse function is demonstrated on specific examples of oscillation theory. The final part offers a view on Laplace transform using MATLAB software.
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OPC client for regulatory control modelling in COMES system
Brzobohatý, Jan ; Šír, Michal (referee) ; Pásek, Jan (advisor)
It was created program of the OPC client which simulates behavior of a continuous dynamical system. The simulated continuous dynamical system is described by the differential equation. The numerical solution of the differential equation simulates response of the dynamical system. The OPC client is connected to the control system with the regulatory program via the OPC server. The response calculated by OPC client and the action of the control system program transferred via OPC communication allow modeling and tuning the continuous control program implemented in the control system.
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Periodic problem for the Duffing equation
Asante, Michael Onwona ; Řehák, Pavel (referee) ; Šremr, Jiří (advisor)
Při matematickém modelování fyzikálních systémů se používají obyčejné diferenciální rovnice různých tvarů. Diferenciální rovnice popisující tyto systémy jsou často složité nelineární rovnice, avšak pomocí vhodných aproximací nelinearity lze odvodit jednoduché rovnice zvané Duffingovy rovnice, které lze analyticky studovat. V matematickém modelování mechaniky problém hledání periodických řešení těchto Duffingových rovnic úzce souvisí s existencí periodických vibrací jeho odpovídajícího nelineárního oscilátoru. V této práci je provedena analýza řešení a existence řešení v autonomních a neautonomních případech uvažované Duffingovy rovnice s podporou simulací v MATLAB.
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