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

 

[charng]

I am happy to provide a response to your question about the Lagrangian for a rheonomic constraint. A rheonomic constraint is a constraint that depends on time, and it can be represented mathematically by a function of the generalized coordinates and time. In terms of the Lagrangian, this means that the constraint will appear as an additional term in the Lagrangian function.

When dealing with a system with a rheonomic constraint, the Lagrangian will indeed change. The additional term representing the constraint will be added to the original Lagrangian, and this will affect the equations of motion derived from the Euler-Lagrange equation.

In terms of the treatment of time, it is important to include it as a generalized coordinate in the Lagrangian. This is because the rheonomic constraint is dependent on time, and therefore, it must be included in the equations of motion. Ignoring time and using the Euler-Lagrange equation normally would not yield accurate results.

In summary, when dealing with a system with a rheonomic constraint, the Lagrangian will change due to the inclusion of the constraint term. Time should also be treated as a generalized coordinate in the Lagrangian to accurately account for the rheonomic constraint. I hope this helps clarify your understanding of the Lagrangian for a rheonomic constraint.