Mechanical systems subjected to velocity-dependent constraints occur frequently. The Frobenius theorem allows us to unequivocally decide whether constraints that depend linearly on the velocities are integrable or not. We show how to formulate the Frobenius integrability condition by means of the theory of exterior differential forms, and illustrate its application to interesting problems in classical mechanics. Finally, we discuss the practical importance of identifying the nature of the constraints as concerns integrability.
Keywords:
velocity-dependent constraints; holonomic constraints; Frobenius integrability condition
