Is this constraint nonholonomic or not?

[qwerfdsazxcv]

I really want to know whether this equation is nonholonomic or not.

(As far as I know, Nonholonomic constraint has a term of velocity and do non-integrable. But this formula does not dependent on a path, because it is a total differential form.)

 

[andrewkirk]

It is nonholonomic, for the reason you gave. Note that the second part of the constraint $df=\frac{\partial f}{\partial q}dq + \frac{\partial f}{\partial q'}dq'+\frac{\partial f}{\partial t}dt=0$ is redundant, as it follows from the first constraint.

 

[zwierz]

Sorry for digging up old story but the correct answer on OP's question is as follows: it depends on the function $f$. For example, if $f=\dot x$ then the constraint is holonomic; if $f=\dot x+y\dot z$ the the constraint is nonholonomic.