München, Techn. Univ., Diss., 2008

Techn. Universiẗat, Diss., 2005--München.

Thesis (Ph. D.)--Universität Leipzig, 1905. / Vita. Includes bibliographical references.

Th. 3e cycle--Méc. non linéaire et chronométrie--Besançon, 1979. N°: 309.

Dissertação (Mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. / Made available in DSpace on 2012-10-17T15:28:58Z (GMT). No. of bitstreams: 0Bitstream added on 2014-09-25T19:17:26Z : No. of bitstreams: 1 170074.pdf: 1661870 bytes, checksum: 1fbfe9c10fdab7889a1cabd91a6a8d2b (MD5) / Estuda os fluxos de Toda generalizados caracterizados pela equação diferencial

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2000-08Bitstream added on 2014-06-13T19:21:27Z : No. of bitstreams: 1 teixeira_rg_dr_ift.pdf: 526804 bytes, checksum: 436dbf87cd5794edcd5c33d1534f2653 (MD5) / Neste trabalho apresentamos um estudo detalhado do formalismo de Hamilton-Jacobi para sistemas singulares, fazendo sua generalização para sistemas com variáveis dinâmicas pertencentes à álgebra de Berezin. Analisamos, em especial, as condições de integrabilidade e sua relação com as condições de consistência no formalismo Hamiltoniano de Dirac. Por fim, estudamos o processo de quantização relacionado a esse formalismo, usualmente interpretado como uma quantificação relacionado a esse formalismo, usualmente interpretado como uma quantificação a gauge livre, e os cuidados que devemos ter com esta interpretação. / In this work we present a detailed study of the Hamilton-Jacobi formalism for singular systems, making its generalization for systems containing dynamical variables which belongs to the Berezin algebra. We analyse, with particular care, the integrability conditions and its relation with consistency conditions in Dirac's Hamiltonian formalism. Finally, we study the quantization process related to this formalism, usually interpreted as a gauge free quantization, and comment the necessity of caution with this interpretation.

In the classical calculus of variations, the Hamilton - Jacobi theory leads, under general hypotheses, to sufficient conditions for a local minimum. The optimal control problem as well has its own Hamilton -Jacobi approach to sufficient conditions for optimality. In this thesis we extend this approach to the differential inclusion problem; a general, nonconvex, nondifferentiable control problem. In particular, the familiar Hamilton - Jacobi equation is generalized and a corresponding necessary condition (chapter 2) is obtained. The sufficiency condition (chapter 3) is derived and an example is presented where it is shown how this result may lead to considerable simplification. Finally, we show (chapter 4) how the classical theory of canonical transformations may be brought to bear on certain Hamiltonian inclusions associated with the differential inclusion problem. Our main tool will be the generalized gradient, a set valued derivative for Lipschitz functions which reduces to the subdifferential of convex analysis in the convex case and the familiar derivative in the C¹ case. / Science, Faculty of / Mathematics, Department of / Graduate

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