Heisenberg and Varying the Velocity

[Trying2Learn]

Good Morning

When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative).

I do understand that this is allowed: we are trying to find the "trajectory" for position and velocity and our trial functions allow us to vary both.

Then, later, came the Heisenberg Uncertainty Principle which states: "that you can never simultaneously know the exact position and the exact speed of an object."

So, my question is:

Did Hamilton "inspire" Heisenberg?
Is there a relationship between these two ideas?
Or is it just coincidence?

 

[PeroK]

Is there a relationship between these two ideas?

There is no direct connection. The idea behind Hamilton's principle is quite subtle, but unrelated to the HUP.