Lagrangian for a rheonomic constraint?

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SUMMARY

The discussion centers on the application of the Lagrangian mechanics framework to systems with rheonomic constraints. It is established that when dealing with a rheonomic constraint, the Lagrangian can still be expressed as L = T - V, where T is the kinetic energy and V is the potential energy. The presence of a time-dependent term in the Lagrangian, L(q, q', t), does not alter the application of the Euler-Lagrange equation, which can be utilized in the same manner as in systems without rheonomic constraints.

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  • Understanding of Lagrangian mechanics
  • Familiarity with Euler-Lagrange equations
  • Knowledge of holonomic constraints
  • Basic concepts of kinetic and potential energy
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  • Study the derivation of the Euler-Lagrange equation in detail
  • Explore the implications of rheonomic constraints in classical mechanics
  • Investigate examples of systems with time-dependent Lagrangians
  • Learn about holonomic versus non-holonomic constraints
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This discussion is beneficial for students and professionals in physics, particularly those studying classical mechanics, as well as researchers focusing on advanced topics in Lagrangian dynamics.

adartsesirhc
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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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