  This paper presents a geometric description on Lie algebroids of Lagrangian
systems subject to nonholonomic constraints. The Lie algebroid framework
provides a natural generalization of classical tangent bundle geometry. We
define the notion of nonholonomically constrained system, and characterize
regularity conditions that guarantee the dynamics of the system can be obtained
as a suitable projection of the unconstrained dynamics. The proposed novel
formalism provides new insights into the geometry of nonholonomic systems, and
allows us to treat in a unified way a variety of situations, including systems
with symmetry, morphisms and reduction, and nonlinearly constrained systems.
Various examples illustrate the results.
