So, I was reading Classical Mechanics by Goldstein where he just introduced scleronomous and rheonomous constraints.
Constraints are further classified according to whether the equations of constraint contain the time as an explicit variable (rheonomous) or are not explicitly dependent on time (scleronomous). A bead sliding in a rigid curved wire fixed in space is obviously subject to scleronomous constraint; if the wire is moving in some prescribed fashion, the constraint is rhenomous. Note that, if the wire moves, say, as a reaction to the bead's motion, then the time-dependence of the constraint enters in the equation of the constraint only through the coordinates of the curved wire. The overall constraint is then scleronomous.
I couldn't get why the case where the wire moves "as a reaction to the bead's motion" is scleronomous.
$\bullet$ Isn't the time-dependence of the constraint enough for the equation of constraint to be schelonomous? (Is there any significance of the word explicit in this present context?)
$\bullet$ Why is the above example of bead-wire not schleronomous? When the wire moves in a "prescribed fashion", the case is rheonomous; but when the wire moves, "as a reaction to the bead's motion", the case becomes sceloronomous. Why is it so? How does the time-dependence by entering "in the equation of the constraint only through the coordinates of the curved wire" make the the equation of constraint rheonomous?