The relation holds true for nonrelativistic systems when all of the following conditions are satisfied ∂ ∂ V ( q , q ˙ ˙ , t ) ∂ ∂ q ˙ ˙ i = 0 , ∀ ∀ i ∂ ∂ T ( q , q ˙ ˙ , t ) ∂ ∂ t = 0 T ( q , q ˙ ˙ ) = ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( c i j ( q ) q ˙ ˙ i q ˙ ˙ j )