It can be verified immediately that Lagrange’s equations (4.75) corresponding to the Lagrangians L(q, q, t ˙ ), L = cL, L = L + dF/dt, with c a constant and F(q, t) an arbitrary C2 function, have the...

It can be verified immediately that Lagrange’s equations (4.75) corresponding to the Lagrangians L(q, q, t ˙ ), L = cL, L = L + dF/dt, with c a constant and F(q, t) an arbitrary C2 function, have the same solutions. To clarify this point, we write explicitly

                              dF dt = q˙ · ∇qF(q, t) + ∂F ∂t .