An algebraic procedure for reducing the Boltzmann-Hamel equations in nonholonomic systems

Nonholonomic systems are increasingly worth considering, because of their application for a wide class of models in mechanical engineering, joint construction, robotics, control for wheels and many other types of mechanisms. A mathematical method suitable for treating such models is based on the definition of quasi--velocities and the formlation of the Boltzmann--Hamel equations. The paper pursues the aim of discussing the appropriate choice of quasi--velocities: the possibility of simplifying the mathematical problem via the definition of specific quasi--velocities is discus\-sed, mainly focussing on the linear structure of part of the system and developing algebraic procedure. The technique formulated in the paper is then applied to some models which are exemplars in literature for nonholonomic constrained systems.