Is it possible to model any physical system with a Lagrangian convex in its velocity variables ?
I am aware that many Lagrangian can model the same system and maybe not all of them are partially convex in their velocity variables, but can we always find one ?
Do we have an understanding about what kinds of systems cannot be described by such a Lagrangian ?
Most of the Lagrangians I worked with have this property which is useful to derive a Hamiltonian through the Legendre transform and I was wondering to which extent this property holds and how fundamental it is ? Do "most" physical systems have it ?
I am aware of similar questions on this forum, I went through them but I don't believe any of the posts really answers my question.
