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1	Μελέτη Hamiltonian μηχανικών δυναμικών συστημάτων με εφαρμογή στο σύστημα σφαίρας-ράβδου Μουστάκης, Νικόλαος 01 February 2013 (has links) Στην παρούσα διπλωματική εργασία παρουσιάζεται η μεθοδολογία εξαγωγής διαφορικών εξισώσεων κατά Hamilton. Οι προκύπτουσες διαφορικές εξισώσεις είναι n το πλήθος (όπου n είναι το πλήθος των βαθμών ελυθερίας του συστήματος) διαφορικές εξισώσεις πρώτου βαθμού και περιγράφουν την δυναμική συμπεριφορά ενός μηχανικού συστήματος. Παρουσιάζεται το εκτενές θεωρητικό πλαίσιο που απορρέει απο τις εξισώσεις του Ηamilton και αξιοποιούνται οι θεωρητικές αρχές κατα την περιγραφή και τον έλεγχο του συστήματος σφαίρας-ράβδου. / In the diploma thesis we present the Hamiltonian formalism in order to derive first order differential equations which represent the dynamical behaviour of a mechanical system. The derived differential equations are n first order equations (where n is the number of system's degrees of freedom). We present the extensive theoretical framework that is derived from the Hamilton's equations which we use so that to describe and control the ball and beam system. Σφαίρα-ράβδος 515.39 Ball and beam Hamilton's equations
2	Discrete Hamilton's equations for thermo-electromagnetic systems Lee, Seunghan 23 January 2012 (has links) Energy methods are used extensively in the formulation of discrete system models. They simplify the systematic integration of diverse kinematic schemes, and are well suited for characterizing complex energy domain coupling effects. Continuum mechanics models are by contrast normally based on partial differential equation descriptions of the physical system. The research presented here develops a new Hamiltonian method for the simulation of distributed parameter electromagnetic and thermo-electromagnetic systems. It expands the application of current system dynamics modeling techniques, to encompass complex distributed parameter electromagnetic systems. / text Discrete energy methods Hamilton's equations Thermo-electromagnetic systems
3	Spacetime as a Hamiltonian Orbit and Geroch's Theorem on the Existence of Fermions Bergstedt, Viktor January 2020 (has links) Over a century since its inception, general relativity continues to lie at the heart of some of the most researched topics in theoretical physics. It seems likely that the coveted solutions to problems like quantum gravity are to be found in an extension of general relativity, one which may only be visible in an alternate formulation of the theory. In this thesis we consider the possibility of casting general relativity in the form of an initial value problem where spacetime is seen as the evolution of space. This evolution is shown to be constrained and of Hamiltonian type. Not all spacetimes are physically acceptable. To be compatible with particle physics, one would like spacetime to accommodate fermions. Here we can take comfort in Geroch’s theorem, which implies that any spacetime that admits a Hamiltonian formulation automatically supports the existence of fermions. We review the elements that go into the proof of this theorem. / Allmän relativitetsteori har i över hundra år legat i teoretiska fysikens framkant. Det är möjligt att lösningarna på öppna problem som kvantiseringen av gravitation går att finna i en utvidgning av allmän relativitetsteori – och kanske uppenbarar sig denna utvidgning bara ur en alternativ formulering av teorin. I den här uppsatsen formuleras allmän relativitetsteori och dess Einsteinekvationer som ett begynnelsevärdesproblem, genom vilket rumtiden kan betraktas som rummets historia. Vi visar att rummets rörelseekvationer är Hamiltons ekvationer med tvångsvillkor. Enligt partikelfysiken bör fermioner kunna finnas till i rumtiden. Härom kan vi åberopa Gerochs sats, enligt vilken rumtider som har en Hamiltonsk formulering också medger fermioner. Vi redogör för huvuddragen i beviset av Gerochs sats. 3+1 ADM black hole canonical quantization Cauchy surface causality differential geometry Einstein-Hilbert action general relativity Geroch globally hyperbolic Hamilton's equations numerical relativity parallelizable SL(2 C) spacetime spinor spin structure SO(1 3) Stiefel-Whitney class tetrad topology Physical Sciences Fysik

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