Lagrangian for a rheonomic constraint?

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In systems with rheonomic constraints, the Lagrangian can still be derived using the standard approach, as long as the constraint is holonomic and the forces are conservative. The Lagrangian takes the form L = T - V, where T is kinetic energy and V is potential energy, and may include a time-dependent term, L(q, q', t). This time-dependent term does not alter the application of the Euler-Lagrange equation. Therefore, time should be treated as a generalized coordinate when using the equation. Overall, the presence of a rheonomic constraint does not fundamentally change the derivation process.
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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.
 
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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
 
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