Is the Cetaev condition inferable?

Abstract: In the context of holonomic constrained systems the identification of virtual displacements is clear and consolidated: this gives the possibility, once the class of displacements have been combined with Newton's equations, to write the correct equations of motion for the constrained system. The method combines d'Alembert principle with the Lagrange formalism. As far as nonholonomic constraints are concerned, the conjecture that dates back to Ceteav actually defines a class of virtual displacements through which the method d'Alebert-Lagrange can be applied again. Much literature is dedicated to the Cetaev 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 expired in a recent publication: our main objective is a critical investigation of the stated result.