Transversality Condition w/ Right End Point Free & Int. Constraints

[Mosis]

Hi, I've been learning about the calculus of variations this term, and we just covered the transversality condition for an optimization problem with the right end point free, as well as the first necessary condition on the augmented Lagrangian for a problem with integral constraints. I'm wondering what the necessary transversality condition is for a problem with integral contraints with the right end point free. I can't find this information in my textbook or anywhere on the internet, and I have two hunches, though I'm not overwhelmingly confident in either.

 

[Mosis]

to put it another way, I wish to know some information about isoperimetric problems with free endpoints, namely the transversality condition at the free end point