Regularity and symmetries of nonholonomic systems

Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are studied within the framework of linearly singular differential equations. Some examples are given, in particular the well-known singular Lagrangian of the relativistic particle, which with the nonholonomic constraint v² = c² yields a regular system.