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## Main Question or Discussion Point

I am now reading Lagrange's equations part in Taylor's Classical Mechanics text.

It says:

When a system of interest involves constraint forces, F_cstr, and all the nonconstraint forces are derivable from a potential energy(U), then the Lagrangian for the system L is L = T - U, where U is the potential energy for the nonconstraint forces only, and thus this definition of L excludes the constraint forces.

Here's the question: How do we know that U in L = T - U is the potential energy for the nonconstraint forces only? Shouldn't it have contribution from constraint forces if some of constraint forces are conservative?

It says:

When a system of interest involves constraint forces, F_cstr, and all the nonconstraint forces are derivable from a potential energy(U), then the Lagrangian for the system L is L = T - U, where U is the potential energy for the nonconstraint forces only, and thus this definition of L excludes the constraint forces.

Here's the question: How do we know that U in L = T - U is the potential energy for the nonconstraint forces only? Shouldn't it have contribution from constraint forces if some of constraint forces are conservative?