Orientadores: Jose Manoel Balthazar / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-04T04:06:35Z (GMT). No. of bitstreams: 1 Peruzzi_NelsonJose_D.pdf: 9438459 bytes, checksum: 1e95acc28fd5e0b87f7b964ca5a2f34e (MD5) Previous issue date: 2005 / Resumo: Neste trabalho, apresenta-se um novo método numérico para aproximar matriz de transição de estados (STM) para sistemas com coeficientes periódicos no tempo. Este método, é baseado na expansão polinomial de Chebyshev, no método iterativo de Picard e na transformação de Lyapunov-Floquet (L-F) e aplica-se na análise da dinâmica e o controle de sistemas lineares e periódicos. Para o controle, aplicam-se dois projetos para eliminar o comportamento caótico de sistemas periódicos no tempo. O primeiro, usa o projeto de controle realimentado baseado na aplicação da transformação L-F, e o objetivo do controlador é conduzir a órbita do sistema para um ponto fixo ou para uma órbita periódica. No segundo, utiliza-se o controle não-linear para bifurcação, e o objetivo, neste caso, é modificar (atrasar ou eliminar) as características de uma bifurcação ao longo de sua rota para o caos. Como exemplo, aplicou-se, com sucesso, a técnica para análise e o controle da dinâmica: num pêndulo com excitação paramétrica, no oscilador de Duffing, no sistema de Rõssler e sistema pêndulo duplo invertido. O método, também, mostrou-se satisfatório na análise e controle de um sistema monotrilho não ideal / Abstract: In thiswork, a new numericalmethodto approximatestatetransitionmatrix(STM) for systems with time-periodic coefficients is presented. This method is based on the expansion Chebyshev polinomials,on the Picard iterationand on the Lyapunov-Floquet transfonnation(transfonnationL-F). It is applied to the dynamicalanalysis and control of linear periodic systems.For the control, two projectsto eliminatethe chaoticbehaviorof time periodic systemsare applied.The first one, uses the feedbackcontroldesignbased on the L-F transfonnation,and the controller'sobjectiveis to drive the orbit of the systemto an equilibriumpoint or a periodicorbit. fu the secondone, the non-lineal control for bifurcations used, and the objective,in this case, is to modify (to put back or to eliminate) the characteristicsof a bifurcation along its route to chaos. As example, the technique for dynamical analysis and control was applied, successfully, to a pendulum with parametric excitement, the Duffing's oscillator,the Rõssler's systemand the inverteddoublependulum The methodwas, also, to be shownsatisfactoryin the analysisand controlof a monorailnon-idealsystem / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

Sei d>3 ein festgewahlten ganzen Zahl. Der Noether-Lefschetz Ort parametrisiert glatte Fläche in P3 mit Picardzahl größer als eins, die Picardzahl einer allgemeinen solchen Fläche. Der Noether-Lefschetz Ort hat unendlich viele irreduzible Komponenten. In den letzten drei Jahrzehnten wurde die Geometrie dieser Komponenten von Ciliberto, Voisin, Green, Griffiths, Harris, Lopez, Maclean, Otwinowska und vielen anderen untersucht. In dieser Arbeit beschaftigen wir uns mit drei Fragen uber die Geometrie dieser Komponenten. Zunächst untersuchen wir nicht reduzierte Komponenten des Noether-Lefschetz Orts. Die Beobachtung führt uns natürlich auf die zweite Frage: Können wir umgekehrt bekannte Beispiele nicht reduzierter Komponenten von Noether-Lefschetz Orts verwenden, um Beispiele nicht reduzierter Komponenten von Hilbert Schemata von Kurven in P3 zu produzieren? Wir haben zwei unterschiedliche Ergebnisse. Eines davon ist eine Verallgemeinerung vom Mumfords berühmtem Beispiel einer generisch nicht reduzierten Komponente des Hilbert Schemas der glatte Kurven in einer Kubik in P3, hin zu Flachen von beliebigem Grad. Das Andere ist, Beispiele nicht reduzierter Komponenten von Hilbert Schemata von Kurven in zu erzeugen, deren allgemeines Element auch nicht reduziert ist. Solche Komponenten wurden bisher nicht intensiv untersucht. Im Gegensatz zu klassischen Ansätzen verwenden wir Techniken aus der Noether-Lefschetz-Theorie. Schließlich untersuchen wir eine Verallgemeinerung der klassischen Noether-Lefschetz Orts, nämlich den Ort der glatten Grad d Flachen in P3 mit Picardzahl mindestens r, wobei 3 < r <d-1. / For a fixed integer d ≥ 4, the Noether-Lefschetz locus parametrizes smooth degree d surfaces in P3 whose Picard number is strictly greater than one, the Picard number of a general such surface. The Noether-Lefschetz locus has infinitely many irreducible components. Over the last three decades, the geometry of these components has been studied by Ciliberto, Voisin, Green, Griffiths, Harris, Lopez, Maclean, Otwinowska and many others. In this thesis, we study in depth three different questions related to the geometry of the Noether-Lefschetz locus. First, we investigate non-reduced components of the Noether-Lefschetz locus. The above observation naturally leads us to the second question: Can we conversely use known examples of non-reduced components of NLd to produce examples of non-reduced components of Hilbert schemes of curves in P3 ? Here, we have two different results. One is the generalization of Mumford’s famous example of a generically non-reduced components of the Hilbert scheme of smooth curves in a cubic surface in P3 , to hypersurface of any degree in P3 . The other is to produce examples of non-reduced components of Hilbert schemes of curves in P3 , whose general element is also non-reduced, a topic not extensively studied in the literature. Different from classical approaches, we use techniques from Noether-Lefschetz theory. Finally, we investigate a generalization of the classical Noether-Lefschetz locus, namely the locus of smooth degree d surfaces in P3 with Picard number at least r for a fixed 3 ≤ r ≤ d − 1.