Review for NeurIPS paper: Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints

I could not find where it was defined. Sorry if I just missed it somewhere. If I should say something more here, I would say that negative examples, if any, could make the discussion more complete. I understand that the proposed parameterization, seemingly just an incremental modification, is advantageous in many problems of physics learning as the Cartesian coordinate is an orthodox representation. Meanwhile, could you elaborate on cases where the proposed parameterization is not really advantageous and constitute such examples numerically?