Lagrangian for a rheonomic constraint?

[adartsesirhc]

How does a Lagrangian change for a system with a rheonomic constraint? As far as I can see in the derivations, it shouldn't seem to matter, but I just want to make sure.

And if I have a rheonomic constraint, what should I do with the time? Should I just ignore it and use the Euler-Lagrange equation normally, or should I treat it is a generalized coordinate?

thanks.

 

[jomoonrain]

in fact we can obtain every thing from the process of the derivation of the Euler-Lagrange equation.
as long as the constraint is a holonomic constraint,and the F is conservative(so F=V's derivative),the L is T-V.
and the follow things have no differences with the situations which have no such rheonomic constraint,except that there may be a time-concerned term,that is L=L(q,q',t),but this term won't affect us to use the Euler-Lagrange equation