This quantity is generally independent of constraints on a system's motion,
This quantity is generally independent of constraints on a system's motion, a fact that d'Alembert used in the original formulation of his namesake principle. The virtual work on a body is given by the vector of variations in the Lagrangian coordinates dotted with this quantity; that's because this quantity's nth component is the applied force on the system dotted into the partial derivative of the displacement with respect to the nth generalized coordinate. FTP, name this derived vector quantity of Lagrangian mechanics, usually denoted by a capital-Q and given by the gradient of the virtual work with respect to the generalized coordinates.
This quantity is generally independent of constraints on a system's motion, a fact that d'Alembert used in the original formulation of his namesake principle.
{generalized force} [prompt on {virtual work} before it’s mentioned]