Nonholonomic Nonlinear Systems: A General Energy Equation

Nonholonomic systems with nonlinear restrictions with respect to the velocities are considered. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The double formulation both by means of the vector of accelerations and the Lagrangian function turns out to be convenient depending on the aspects and the properties to be pointed out. The main point of the paper is the balance of the mechanical energy induced by the equations of motion; the conservation of the energy on the basis of the tipology of the constraint equations is discussed. The special form of the energy equation allows to identify the categories of nonlinear constraints which entail the conservation of energy.