We search for a cause in everything, it is hard for us to accept that nature doesn’t have a plan. Lagrangians/Hamiltonians seem to work very well in mechanics. I have used a similar approach to model arm movements for ‘normals’ and ‘not-normals’.
The methodology in nutshell is as simple as this, when we move our arm to do a task I assume we are minimizing a cost function. But! as I don’t know this cost function I use data and Inverse-optimal control (fancy term for searching the cost function that governs motion). This lets me produce a set of cost functions that govern the motion for different groups of people.
What I find is that there is a significant difference between two groups and there is also some intragroup variability. This says something deep? 🙂 that probably there is nothing deep in motor control. No central principle by which the motion happens. Evolution is a ‘nonoptimal’ process, therefore, we should accept for these nonprincipled theories in biology.
For those who are pedantic: Read cost functions as cost functionals.