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But, how to compose such a Lagrangian? Everywhere, where I found, it is only assumed and then equation

##d/dt (\partial L/\partial \dot{x})-(\partial L/\partial x)=0## is used.

But, why L=T-V, is this only guessing, or is there any logic, because H=T+V is calculated afterwards. Why T and V are already specified at L? Is it possible to equate L with something, when we do not know that kinetic and potencial energy exist?