# who was the first to discover the Hamilton principle of classical physics?

Who, besides Hamilton, was instrumental in discovering at least part of the so-called Hamilton principle?

$$\delta \int_{a}^{b}L(q,\dot q ,t )dt$$

where $L=T-V$, the Lagrangian.

What exactly, was Lagrange's role, especially in the part that bears his name?

Also, I think that the pure Hamilton's Principle should be written as the stationary action: $$\frac{\delta S}{\delta q_i(t)} = 0$$ Where the action $S$ is written as you have in your post with the time integral of the Lagrangian.