I've learned that Newtonian mechanics and Lagrangian mechanics are equivalent, and Newtonian mechanics can be deduced from the least action principle.
Could the least action principle $\min\int L(t,q,q')dt$ in mechanics be deduced from Newtonian $F=ma$?
Sorry if the question sounds beginnerish
Answer
You also need an expression for the Lagrangian, which in classical mechanics is $$ L = T - U$$
Where $T$ is the kinetic energy and $U$ is the potential energy.
Provided that you can associate a potential $U$ to the force $\vec{F}$ such that $\vec{F} = - \vec{\nabla} U$ (such a force is said to be conservative), the principle of least action and Newton second's law are equivalent.
The demonstration for a single particle in 1D ($T = m v_x^2 /2$, $F = -dU(x)/dx$) is actually a good exercise.
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