Departament de Matemàtiques

Comparteix:

2008

16-18 December 2008
International Young Researchers Workshop on Geometry, Mechanics and Control, Department of Applied Mathematics IV, UPC, Barcelona
Campus Nord UPC, edifici C3, room 005

24-28 November 2008   master course
Manuel F. Rañada, Department of Theoretical Physics, University of Zaragoza
Hamiltonian systems: integrability and separability [notes pdf 519 KiB, 115 pp]
Facultat de Matemàtiques i Estadística, aula 007. 
Schedule: 
Monday, Wednesday, Thursday: 16-18; Tuesday, Friday: 12-14.
Contents  
  • Symmetries and constants of motion
  • Hamilton-Jacobi theory
  • The Kepler problem and the harmonic oscillator
  • Separable systems
  • Super-integrable systems
  • Nonseparable integrable systems
  • Integrable systems and Lax equations
  • Toda lattice and Calogero system
  • Lax formalism and Toda-related systems
  • Hamiltonian systems and symplectic formalism

Basic bibliography  
  • M. Tabor, Chaos and integrability on nonlinear dynamics, Wiley (1989)
  • A.M. Perelomov, Integrable systems of classical mechanics and Lie algebras, Birkhauser (1990)
  • G. Marmo, E.J. Saletan, A. Simoni, B. Vitale, Dynamical systems: A differential geometric approach to symmetry and reduction, Wiley (1985)

15 May 2008
María Barbero Liñán, Department of Applied Mathematics IV, UPC, Barcelona
Strict abnormality in nonholonomic mechanical control systems
Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 12 h
Abstract:   In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal.   The key point for this classification is how those extremals depend on the cost function.   We focus on nonholonomic control mechanical systems and the associated kinematic systems as long as they are equivalent. 
With all this in mind, first we study conditions to relate an optimal control problem for the mechanical system with another one for the kinematic system.   Then, Pontryagin's maximum principle will be used to connect the abnormal extremals of both optimal control problems. 
An example is given to glimpse what the abnormal solutions for kinematic systems become when they are considered as extremals to the optimal control problem for the corresponding nonholonomic mechanical systems.

16 January 2008
Jaume Franch, Department of Applied Mathematics IV, UPC, Barcelona
Differential flatness, a method to design and control mechanical systems
Campus Nord UPC, edifici C3, aula 005; 12 h
Abstract:   A fully actuated machine can execute any joint trajectory in its configuration space.   If the system is under-actuated, only those joint trajectories are allowed which require vanishing inputs at the joints with missing actuators.   However, if the governing dynamics of the under-actuated system is shown to be differentially flat, point-to-point maneuvers of the system in the state space can be constructed by choosing trajectories in the differentially flat output space.   Definitions, equivalences, characterizations and examples of flat systems will be given in this talk.