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UID:news264@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T220655
DTSTART;TZID=Europe/Zurich:20140704T110000
SUMMARY:Seminar in Numerical Analysis: Luis Garcia Naranjo (UNAM\, Mexico C
 ity)
DESCRIPTION:In mechanics\, constraints that restrict the possible configura
 tions of the system are termed holonomic. A simple example is the fixed le
 ngth of the rod of a pendulum. Mechanical systems with constraints on the 
 velocities that do not arise as constraints on positions are called nonhol
 onomic. These often arise in rolling systems\, like a sphere rotating with
 out slipping on a table.\\r\\nThe study of nonholonomic mechanical systems
  is challenging because the equations of motion are not Hamil- tonian. The
  dynamics of the system can however be described in terms of a bracket of 
 functions that fails to satisfy the Jacobi identity. One now speaks of an 
 almost Poisson bracket.\\r\\nThe failure of the Jacobi identity leads to p
 henomena that are not shared by usual Hamiltonian systems. Open questions 
 in nonholonomic mechanics that have received attention in recent years inc
 lude determining general conditions for measure preservation\, existence o
 f asymptotic equilibria\, relationship between symmetries and con- servati
 on laws\, reduction\, and integrability.\\r\\nIn the first part of this ta
 lk I will present a basic introduction to nonholonomic mechanics. I will t
 hen present my recent work with Y. Fedorov and J. C. Marrero in which we s
 tudy the problem of measure preservation for nonholonomic systems possessi
 ng symmetries in a systematic manner. Our method allows us to identify spe
 cific parameter values for which there exists a preserved measure for conc
 rete mechanical examples.
X-ALT-DESC:In mechanics\, constraints that restrict the possible configurat
 ions of the system are termed holonomic. A simple example is the fixed len
 gth of the rod of a pendulum. Mechanical systems with constraints on the v
 elocities that do not arise as constraints on positions are called nonholo
 nomic. These often arise in rolling systems\, like a sphere rotating witho
 ut slipping on a table.\nThe study of nonholonomic mechanical systems is c
 hallenging because the equations of motion are not Hamil- tonian. The dyna
 mics of the system can however be described in terms of a bracket of funct
 ions that fails to satisfy the Jacobi identity. One now speaks of an almos
 t Poisson bracket.\nThe failure of the Jacobi identity leads to phenomena 
 that are not shared by usual Hamiltonian systems. Open questions in nonhol
 onomic mechanics that have received attention in recent years include dete
 rmining general conditions for measure preservation\, existence of asympto
 tic equilibria\, relationship between symmetries and con- servation laws\,
  reduction\, and integrability.\nIn the first part of this talk I will pre
 sent a basic introduction to nonholonomic mechanics. I will then present m
 y recent work with Y. Fedorov and J. C. Marrero in which we study the prob
 lem of measure preservation for nonholonomic systems possessing symmetries
  in a systematic manner. Our method allows us to identify specific paramet
 er values for which there exists a preserved measure for concrete mechanic
 al examples. 
DTEND;TZID=Europe/Zurich:20140704T120000
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