>>12518086be Turing complete?
>>12518097The Lagrangian here is a map
,
i.e. "a function "
The derivative "" is , so you don't need to worry about correlations between and here.
There's the ubiquitous habit of also denoting then t-parametrized value "", a function
by , so don't get confused.
Also don't mix up partial derivatives, as in , with total ones, as in
Lastly, there's variations of functionals , where e.g. , so don't confuse those either.
If you read a good of physics textbooks, you'll get very confused with d'Alembert's principle (and if you watch random undergrads on youtube you'll get away with the idea that it's just a trivial rewrite of Newton, so I'm already sceptical). If you read a math textbook you'll have some work bringing those together with the physics books but if you look into the post Arnold slash control theory slash theoretical engineering, say, diff geo formulations that make it rigorous, you get
https://en.wikipedia.org/wiki/Virtual_displacement#Definitionso just learn the rules and don't mix up .
And with that said, watch out for L's that are neither maps on nor but actually functionals eating .
(So is not that you want to compute, but you could probably give meanint to it via some diract delta functionals)
