Introduction

The research on mechanical and dynamical systems has had a deep impact in other research areas and in the development of several technologies. A big part of its advances has been based on numerical and analytical techniques. In the sixties, the most sophisticated and powerful techniques coming from Geometry and Topology were used in the study of dynamical systems. Those techniques led, for instance, to the beginning of the modern Hamiltonian Mechanics. Geometric techniques have been also applied to a wide range of control problems such as locomotion systems, robotics, etc. Most of these ideas have been developed in the last 30 years by mathematicians of a high scientific level such as J. Marsden, A. Weinstein, R. Abraham, V. Arnold or R. Brockett among others.