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Analytical representation of congruent transformations at high schools
Ptáčková, Tereza ; Robová, Jarmila (advisor) ; Hromadová, Jana (referee)
This work deals with analytical representation of congruent transforma- tion in a plane at high schools. The work is a web page, it contains several interactive components which help student to understand the problem like hyperlinks, stepping of the construction, applets, etc. The work contains several solved problems. Main emphasis is placed on the connection of the synthetic and the analytic approach to congruent transformation. The work uses knowledge of analytic geometry students learn at high school. The web page is aimed at talented students of high school and for teaching at mathematical class. 1
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Building Model Generator for Open Street Maps
Galacz, Roman ; Poulíček, Zbyněk (referee) ; Polok, Lukáš (advisor)
This work concerns obtaining data from the maps provided by the project OpenStreetMap. The data are converted from the format of geographical latitude and longitude to the Cartesian coordinate system. This work also concerns building type recognition in build-up area which are situated on the downloaded map. Part of the work is a demonstration application which is able to model 3D geometry of the buildings, based on the results of the recognition algorithms and also creates a terrain in which these buildings are situated. Generated model is displayed using the OpenGL graphics library.
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Safety of a Commercial Aircraft after Damage to Airframe due to Terrorist Attack
Lošťák, Miroslav ; Petrásek, Miloslav (advisor)
Modern-day terrorist attacks present a considerable danger for commercial aircrafts. This thesis analyzes potential methods of such attacks with a critical analysis of the most dangerous type: an attack from the outside of the aircraft via a fragmentation missile warhead. Such missiles cause damage to the airframe of the aircraft through fragments created by the explosion. In this thesis, analytical geometry is used to determine the area of the aircraft affected by the fragmentation. The aircraft’s geometry and the fragments’ dispersion are calculated by analytical functions, and the effect of the damage is analyzed. A shooting experiment was also carried out, in which fragments were shot at a reinforced skin panel that was manufactured according to the real design of commercial aircraft. The results of the experiment revealed that only directly hit sections of the structure are damaged. Data obtained by the experiment was then used for the creation and improvement of the model used in the simulation by means of the finite element method. This model is used for the numerical calculation of the damage sustained. Further included in the thesis is an analysis of the change in the load-bearing capacity after such an attack. The relationship between the size of the damage and its effect on the load-bearing capacity of the component as well as the entire structure is defined. First, the effect of component damage is analyzed via the FMEA/FMECA methods. This analysis is then extended using fuzzy logic. Fuzzy logic analysis is based on the determination of the size of the damaged component area and the component’s importance on the structure’s carry loads. Application of the defined approach is described for several parts of an aircraft’s life cycle, including development, operation after the terrorist attack, and assessment of causes after a crash caused by a fragmentation missile warhead.
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Safety of a Commercial Aircraft after Damage to Airframe due to Terrorist Attack
Lošťák, Miroslav ; Salga, Jaroslav (referee) ; Kusák,, Jan (referee) ; Petrásek, Miloslav (advisor)
Modern-day terrorist attacks present a considerable danger for commercial aircrafts. This thesis analyzes potential methods of such attacks with a critical analysis of the most dangerous type: an attack from the outside of the aircraft via a fragmentation missile warhead. Such missiles cause damage to the airframe of the aircraft through fragments created by the explosion. In this thesis, analytical geometry is used to determine the area of the aircraft affected by the fragmentation. The aircraft’s geometry and the fragments’ dispersion are calculated by analytical functions, and the effect of the damage is analyzed. A shooting experiment was also carried out, in which fragments were shot at a reinforced skin panel that was manufactured according to the real design of commercial aircraft. The results of the experiment revealed that only directly hit sections of the structure are damaged. Data obtained by the experiment was then used for the creation and improvement of the model used in the simulation by means of the finite element method. This model is used for the numerical calculation of the damage sustained. Further included in the thesis is an analysis of the change in the load-bearing capacity after such an attack. The relationship between the size of the damage and its effect on the load-bearing capacity of the component as well as the entire structure is defined. First, the effect of component damage is analyzed via the FMEA/FMECA methods. This analysis is then extended using fuzzy logic. Fuzzy logic analysis is based on the determination of the size of the damaged component area and the component’s importance on the structure’s carry loads. Application of the defined approach is described for several parts of an aircraft’s life cycle, including development, operation after the terrorist attack, and assessment of causes after a crash caused by a fragmentation missile warhead.
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Simulation of dose distribution irradiation
Večeřa, Petr ; Hlaváč, Martin (referee) ; Kolářová, Jana (advisor)
This project deals with the issue of simulation of dose irradiation. This principle is used in a radiotherapeutic device known as a Leksell Gamma Knife for the treatment of intracranial tumours. With regard to the theoretical observations obtained by studying this device, the project suggests the use of analytical geometry for the creation of a mathematical model for calculation of the intensity in the rayed area. A demonstration program Leksell_xvecer08 has been created for this model in a MatLab software background, which enables the user to change various input arguments and simulate a picture of the dosage spread in the target scanned areas.
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Use of means of the program Maple in lessons of analytical geometry
BABKOVÁ, Petra
The content of this diploma is to create applications called maplets. The maplets are used to show influences of the coefficients in equation to their representation. The maplets are programmed in the program Maple. These tools should make teaching analytical geometry easy at high schools and in introductory university courses.
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