March  2010, 3(1): i-i. doi: 10.3934/dcdss.2010.3.1i

Preface

1. 

Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28006 Madrid, Spain

2. 

Department of Fundamental Mathematics, Faculty of Mathematics, University of La Laguna, C/Astrofisico Fco. Sanchez s/n, 38071, La Laguna, Tenerife, Canary Islands, Spain

3. 

Instituto de Ciencias Matematicas, C/ Serrano 123, 28006 Madrid, Spain

Published  December 2009

Nonholonomic mechanics describes the motion of systems with constraints on velocities that are not derivable from position or geometric constraints. The best known examples of such systems are rolling balls or disks and the sliding skate. Nonholonomic constraints have been the subject of deep analysis since the dawn of Analytical Mechanics. Recently, many authors have shown a new interest in that theory and also in its relation to the new developments in control theory, subriemannian geometry, robotics, etc. The main characteristic of this period is that geometry has been used in a systematic way.
   Optimal control theory and geometry have also strongly influenced each other. This relationship begins with the formulation of the Maximum principle in the 1950's, initiating a geometrization program of optimal control theory which continues nowadays. It is now usual to work in optimal control theory using a differential geometric language (Lie algebras and Lie groups, integral manifolds, symplectic structures, riemannian and subriemannian geometries, homogeneous spaces...).

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Citation: Manuel de León, Juan C. Marrero, David Martin de Diego. Preface. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : i-i. doi: 10.3934/dcdss.2010.3.1i
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