Let's consider a system of $N$ point particles. Let's also assume that acceleration of each particle is a function of positions of all the particles.
I assume that for such a system we can prove that the motion of the system is described by Lagrangian equations of motion.
How exactly can it be done?
ADDED
I do not ask why Lagrangian is defined as $L = T - V$. What I am interested is how to derive Lagrangian equations of motion from Newtonian equations of motion.
