Summing (this multiplied by q ˙ ˙ l ) over l results in ∑ ∑ l = 1 n ( ∂ ∂ T ( q , q ˙ ˙ ) ∂ ∂ q ˙ ˙ l q ˙ ˙ l ) = ∑ ∑ l = 1 n ( ( ∑ ∑ i = 1 n ( c i l ( q ) q ˙ ˙ i ) + ∑ ∑ j = 1 n ( c l j ( q ) q ˙ ˙ j ) ) q ˙ ˙ l ) = ∑ ∑ l = 1 n ∑ ∑ i = 1 n ( c i l ( q ) q ˙ ˙ i q ˙ ˙ l ) + ∑ ∑ l = 1 n ∑ ∑ j = 1 n ( c l j ( q ) q ˙ ˙ j q ˙ ˙ l ) = ∑ ∑ i = 1 n ∑ ∑ l = 1 n ( c i l ( q ) q ˙ ˙ i q ˙ ˙ l ) + ∑ ∑ l = 1 n ∑ ∑ j = 1 n ( c l j ( q ) q ˙ ˙ l q ˙ ˙ j ) = T ( q , q ˙ ˙ ) + T ( q , q ˙ ˙ ) = 2 T ( q , q ˙ ˙ )