Subtracting potential from kinetic energy? It feels like a measure of how much of a budget is unspent, how much is left to drive deviations from a trajectory...
That feels like finance. There ought to be applications of the Lagrangian to the world of financial modeling.
Once upon a time, that's where the thought would have ended. An idle speculation. Today, though, the answer is a few keystrokes away: google.com/search?q=lagrangian+finance.
73,800 hits. Yeah, looks like there's an application or two.
We don't truly grok the web. Not yet.