On the Četaev Condition for Nonholonomic Systems

In the context of holonomic systems, the identification of virtual displacements is clear and consolidated. This provides the possibility, once the class of displacements have been coupled with Newton’s equations, for us to write the correct equations of motion. This method combines the d’Alembert principle with Lagrange formalism. As far as nonholonomic systems are concerned, the conjecture that dates back to Cˇetaev actually defines a class of virtual displacements through which the d’Alembert–Lagrange method can be applied again. A great deal of literature is dedicated to the Cˇetaev rule from both the theoretical and experimental points of view. The absence of a rigorous (mathematical) validation of the rule inferable from the constraint equations has been declared to have expired in a recent publication; one of our objectives is to produce a critical comment on this stated result. Finally, we explore the role of the Cˇetaev condition within the significant class of nonholonomic homogeneous constraints.