2000
- 20 December 2000
- Miguel C. Muñoz Lecanda, Department of Applied Mathematics IV, UPC
- Nonholonomic systems and control
- Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca); 15.30 h
- Abstract:
- 15 November 2000
- Jesús Marín, Dept. of Economical Mathematics, University of Barcelona
- Characterization of constraints for singular lagrangians on jet bundles
- Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca); 15.30 h
- Abstract: Given a non-autonomous singular dynamical system defined on a fibred manifold, different characterizations of constraints obtained from the constraint algorithm are given. As particular cases, singular lagrangians and their related hamiltonian formalisms are studied.
- 11 October 2000
- Igor Kanatchikov, Center of Theoretical Physics, Polish Academy of Sciences
- Towards geometric quantization and the Schroedinger functional in the pre-canonical approach
- Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca); 15.30 h
- Abstract: We will review the structures of the pre-canonical (De Donder-Weyl) Hamiltonian formalism in field theory, mainly concentrating on Poisson-Gerstenhaber brackets of dynamical variables represented by differential forms. Possible approaches to quantization, mainly a heuristic (pre-)canonical and geometric, are outlined. A generalization of the prequantization formula to Poisson-Gerstenhaber algebra of differential forms will be presented. A relation between a wave function arising within the precanonical approach and the Schroedinger functional of the canonical field quantization will be discussed in detail.
- 27 September 2000
- Rafael Ramírez, Department of Computer Engineering and Mathematics, Universitat Rovira i Virgili
- On the dynamics of nonholonomic systems
- Dep. de Matemàtica Aplicada i Telemàtica, Campus Nord UPC, edifici C3, 204a (biblioteca de matemàtiques); 15.30 h
- Abstract: We propose a new mathematical model to describe the behaviour of the mechanical systems with constraints (the model is obtained as reduction of the Lagrangian equations). The possibility of studying the nonholonomic systems by using the Cartesian approach is analyzed. The results obtained are illustrated in concrete examples (a nonholonomically constrained particle in the space, Chapligin-Caratheorody's sleigh, Gantmakher's system).
- 19 July 2000
- Jaime Keller, Center for Computational Materials Science, Technische Universität Wien and
Div. de Ciencias Básicas, Facultad de Química, and Facultad de Estudios Superiores-Cuautitlán, Universidad Nacional Autónoma de México (permanent address) - A geometric theory of carriers in spacetime
- Dep. de Matemàtica Aplicada i Telemàtica, Campus Nord UPC, edifici C3, 204a (biblioteca de matemàtiques); 15.30 h
- Abstract: A comprehensive geometric theory of fields of carriers of energy is formulated from the basic principles of relativity theory extended to include action (START). The approach shows the basic role of carriers of energy in the geometrical formulation of the description of test particles in spacetime. Besides illustrating the basic principles of general relativity, our approach also contains, being a deductive theory, results of density functional theory, wave function quantum mechanics, the classical theory of particles and the fundamentals of their in electrodynamics (electroweak and color) interactions. The formalism is a geometric selfcontained theory of test particles.
- 08 March 2000
- Jaume Franch, Department of Applied Mathematics and Telematics, UPC
- Linearization by prolongations of two-inputs driftless systems
- Dep. de Matemàtica Aplicada i Telemàtica, Campus Nord UPC, edifici C3, 204a (biblioteca de matemàtiques); 15.30 h
- Abstract: This seminar deals with the problem of linearization by prolongations of two-input driftless systems. Although for general two-input systems the number of computations needed to know if a system is linearizable by prolongations is quite high, for driftless systems the condition that we have found needs very few computations. Some real systems are proven to fulfill this condition, such as the unicycle, a planar robot and a hopping robot.
- 19 January 2000
- Carles Batlle, Department of Applied Mathematics and Telematics, UPC
- Control in Lie groups
- Dep. de Matemàtica Aplicada i Telemàtica, Campus Nord UPC, edifici C3, 204a (biblioteca de matemàtiques); 15.30 h
- Abstract: Drift-free systems with fewer controls than state variables arise in a variety of problems in nonlinear control and many of them can be, roughly speaking, formulated as a dynamical system on a Lie group with the control belonging to the corresponding Lie algebra. From a more geometrical point of view, this can be expressed in terms of the so called "kinematical" connection for a nonholonomic constrained system [1][2]. We review here the essential concepts as well as a constructive control method based on averaging theory with sinusoid inputs [3].
[1] Ostrowski, J.P., "The mechanics and control of undulatory robotic locomotion", Ph. D. Thesis, California Institute of Technology (1996).
[2] Kelly, S.D., and R.M. Murray, "Geometric phases and robotic locomotion", CDS Tech. Rep. 94-014, California Institute of Technology (1994).
[3] Leonard, N.E., and P.S. Krishnaprasad, "Averaging for attitude control and motion planning", Proc. of the 32nd IEEE Conference on Decision and Control, pp. 3098-3104 (1993).
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