I probably used a wrong word. I meant the action.

In Taylors book chapter 7 equation 7.8

I really just made up a simple example to see if I could calculate the action to see if I was understanding it correctly.

The basic idea is that I compute T-V for all points $ t_1 < t < t_2 $ (or at least a sampling of them). If x = f(t) and $ v = \dot{x} $ then given that $ T = \frac{1}{2} m v^2 $ then this should just be the slope of the line on the x-t graph at that point squared. V is of course the potential defined at every point x.

However I am noticing some peculiarities, namely that x=0 is a solution and therefore it's going to be interesting finding a stationary functional that's not that.

I'm currently working on a Jupyter notebook to see.