02162nam 2200241 n 450 001001100000049001300011100004000024200009500064210003700159300006100196328007000257330116400327336002001491689003501511700002401546702001801570702001901588801001801607856027401625997000701899FMT000701906FOR000701913TD12025519 aTDMAGDIG a20190501d2010------k--ita-50----ba 1 aConstrained Calculus of Variations and Geometric Optimal Control TheorybTesi di dottorato 1cUniversity of Trentod2010-02-05 aIn relazione con http://eprints-phd.biblio.unitn.it/170/ 0btesi di dottoratocMAT/07 FISICA MATEMATICAeUniversity of Trento aThe present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on the introduction of the bundle of affine scalars over the configuration manifold, is then presented. The analysis includes a revisitation of Pontryagin Maximum Principle and of the Erdmann-Weierstrass corner conditions, a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system and a generalization of the classical criteria of Legendre and Bliss for the characterization of the minima of the action functional to the case of piecewise-differentiable extremals with asynchronous variation of the corners. aapplication/pdf0 aMAT/07bFISICA MATEMATICAcTDR 0aLuria, Gianvittorio 0aMassa, Enrico 0aPagani, Enrico 3aITbIT-FI00984 uhttp://memoria.depositolegale.it/*/http://eprints-phd.biblio.unitn.it/170/1/Constrained_Calculus_of_Variations_and_Geometric_Optimal_Control_Theory.pdf2http://eprints-phd.biblio.unitn.it/170/1/Constrained_Calculus_of_Variations_and_Geometric_Optimal_Control_Theory.pdf aCF aTD aTD