# Nonholonomic constraints

1. Jan 11, 2012

### 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.

Last edited: Jan 11, 2012
2. Jan 11, 2012

### 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.

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