  The purpose of this paper is to show that, at least for Lagrangians of
mechanical type, nonholonomic Euler-Lagrange equations for a nonholonomic
linear constraint D may be viewed as non-constrained Euler-Lagrange equations
but on a new (generally not Lie) algebroid structure on D. The proposed novel
formalism allows us to treat in a unified way a variety of situations in
nonholonomic mechanics and gives rise to a version of Neoether Theorem
producing actual first integrals in case of symmetries.
