A generalization of the Chetaev condition for nonlinear nonholonomic constraints: The velocity-determined virtual displacement approach

We present a formalism for nonlinear nonholonomic mechanical systems that generalizes the Chetaev model. Our treatment of the constrained problem is based on the velocity-determined virtual displacements. As an example, we discuss the Apell-Hamel dynamical system in the frame of a moving elevator and find the present method to provide results consistent with Newtonʹs solution, in contrast to the other treatment generalizing the Chetaev condition based on a direct velocity expansion of the constraint equation. The known Chetaev condition follows as a special case of our scheme when the constraint is homogeneous in relative velocities.