in which ⁠ ∂ / ∂ q ⁠ = (⁠ ∂ / ∂ q 1 ⁠, ⁠ ∂ / ∂ q 2 ⁠, …, ⁠ ∂ / ∂ q N ⁠) is a shorthand notation for a vector of partial derivatives with respect to the indicated variables (see for example matrix calculus for this denominator notation), and possibly time t,