Resulting in T ( q , q ˙ ˙ ) = 1 2 ∑ ∑ k = 1 N ( m k ( ∑ ∑ i = 1 n ( ∂ ∂ r k ( q ) ∂ ∂ q i q ˙ ˙ i ) ⋅ ⋅ ∑ ∑ j = 1 n ( ∂ ∂ r k ( q ) ∂ ∂ q j q ˙ ˙ j ) ) ) = ∑ ∑ k = 1 N ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( 1 2 m k ∂ ∂ r k ( q ) ∂ ∂ q i ⋅ ⋅ ∂ ∂ r k ( q ) ∂ ∂ q j q ˙ ˙ i q ˙ ˙ j ) = ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( ∑ ∑ k = 1 N ( 1 2 m k ∂ ∂ r k ( q ) ∂ ∂ q i ⋅ ⋅ ∂ ∂ r k ( q ) ∂ ∂ q j ) q ˙ ˙ i q ˙ ˙ j ) = ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( c i j ( q ) q ˙ ˙ i q ˙ ˙ j )