On a symplectic manifold, this quantity is given by applying the tautological one-form to a Hamiltonian vector field. In a system with non-holonomic constraints, the change in quantity is equal to the negative sum of virtual work integrals along a constraint path. An “abbreviated” form of this quantity that is not parameterized by time is constant by Maupertuis’s (“mo-pair-TWEE’s”) principle. Hamilton’s principal function is equal to this quantity, (10[2])whose negative time derivative is equal to the Hamiltonian by the Hamilton–Jacobi (“jah-KOH-bee”) equation. The derivation of the Euler–Lagrange equation assumes that this quantity is constant (10[1])under small perturbations. This quantity is defined as the time integral of the Lagrangian. (10[2])For 10 points, (10[1])name this quantity that is minimized along paths taken by a free particle. (0[3])■END■