How to derive the linear form of Pfaffian equation?

I am working on fundamental dynamics in last few days. The question is about Pfaffian constraint.

A general form of Pfaffian constraint is
$$ A(q)^{mathrm{T}}d{q} + b(q)dt = 0tag{1}$$
which is formed as
$$ A(q)^{mathrm{T}} delta q = 0tag{2}$$ with variation theorem, i.e. $$b(q)dt=0.tag{3}$$

However, in some applications such as non-holonomic system, that the Pfaffain form is simply given by
$$A(q)^{mathrm{T}}dot{q} = 0.tag{4}$$
I simply want the detailed derivation of this form. After searching internet, I didn’t find too much things helpful to the derivation of this form.