Can nonholonomic constraints always be expressed as inequalities?

[espen180]

So far, every nonholonomic constraint I have seen can be expressed as a collection of inequalities involving the coordinates of the system. For example, a small ball rolling down a sphere with radius a has the constraint $r^2-a^2\geq 0$, where r is the radial coordinate of the ball.

Can every nonholonomic constraint be written in this form? If not, I would appreciate a counterexample.

Thanks in advance.

 

[Bill_K]

espen180, Nonholonomic means nonintegrable. They can be inequalities, but often they are relationships involving the velocities which can't be integrated to yield a relationship between coordinates. For example when an object rolls without slipping on another, the constraint is an equality between the tangential velocities. Picture a quarter standing up and rolling around on a tabletop.