Nonholonomic constraints: A new viewpoint

Abstract

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 nonconstrained 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 Noether theorem producing actual first integrals in the case of symmetries.