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Solved Problems in Theoretical Mechanics
Roskot, Michal ; Koupilová, Zdeňka (advisor) ; Snětinová, Marie (referee)
The object of the bachelor's thesis was the creation of tasks for "Collection of Solved Problems in Physics". I have created 20 structured tasks on the subject of theoretical mechanics. These are mostly on a university level. I have successfully filled the chapters "The Principle of virtual work" and "Hamiltonian mechanics", which are included in the subject of theoretical mechanics. In order to create the bachelor's thesis it was necessary to get familiar with the web interface of the "Collection". At the same time to create pictures I had to learn to work with a graphical editor. In the text of the bachelor's thesis I characterize the technical solution of "Collection of Solved Problems in Physics", describe advantages of the used structure of the solved tasks and I briefly summarize content of the individual tasks.
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Application of the Nambu mechanics formalism in atmospheric dynamics
Procházková, Zuzana ; Šácha, Petr (advisor) ; Badin, Gualtiero (referee)
Nambu mechanics is a generalization of Hamiltonian mechanics that uses multiple conserved quantities as Hamiltonians. In this thesis, we review Nambu mechanics and its application on the equations of incompressible flow and shallow water equations. The Nambu form of the equations of incompressible flow is guessed based on its Hamiltonian form and derived conserved quantities. With the example of the shallow water equations a more general method of Nambu form derivation is illustrated. Based only on the knowledge of the Hamiltonian and the potential enstrophy moments conservation, the shallow water equations are written as a sum of the Nambu brackets and a Poisson bracket. For the classical potential enstrophy, the derived equations are up to constant factors equivalent to the known form of the shallow water equations. The notation by antisymmetric Nambu brackets is convenient for finding conservative schemes and the theory can be also used for example for the study of deviations of flow from stationary flow.
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Application of the Nambu mechanics formalism in atmospheric dynamics
Procházková, Zuzana ; Šácha, Petr (advisor) ; Badin, Gualtiero (referee)
Nambu mechanics is a generalization of Hamiltonian mechanics that uses multiple conserved quantities as Hamiltonians. In this thesis, we review Nambu mechanics and its application on the equations of incompressible flow and shallow water equations. The Nambu form of the equations of incompressible flow is guessed based on its Hamiltonian form and derived conserved quantities. With the example of the shallow water equations a more general method of Nambu form derivation is illustrated. Based only on the knowledge of the Hamiltonian and the potential enstrophy moments conservation, the shallow water equations are written as a sum of the Nambu brackets and a Poisson bracket. For the classical potential enstrophy, the derived equations are up to constant factors equivalent to the known form of the shallow water equations. The notation by antisymmetric Nambu brackets is convenient for finding conservative schemes and the theory can be also used for example for the study of deviations of flow from stationary flow.
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Solved Problems in Theoretical Mechanics
Roskot, Michal ; Koupilová, Zdeňka (advisor) ; Snětinová, Marie (referee)
The object of the bachelor's thesis was the creation of tasks for "Collection of Solved Problems in Physics". I have created 20 structured tasks on the subject of theoretical mechanics. These are mostly on a university level. I have successfully filled the chapters "The Principle of virtual work" and "Hamiltonian mechanics", which are included in the subject of theoretical mechanics. In order to create the bachelor's thesis it was necessary to get familiar with the web interface of the "Collection". At the same time to create pictures I had to learn to work with a graphical editor. In the text of the bachelor's thesis I characterize the technical solution of "Collection of Solved Problems in Physics", describe advantages of the used structure of the solved tasks and I briefly summarize content of the individual tasks.
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