Virtual work

Virtual work is the work of applied forces through an infinitesimal displacement compatible with the system's instantaneous constraints. Equilibrium or overdamped force balance requires the total virtual work to vanish for every admissible virtual displacement.

Generalized forces are the coefficients of virtual work in a set of generalized coordinates. A translational coordinate has a force as its coefficient, while an angular coordinate has a torque. A generalized force conjugate to $q_i$ has units of energy divided by the units of $q_i$. Forces not already included in the Lagrangian enter the Euler-Lagrange equations as $d(\partial L/\partial {\dot{q}}_i)/dt-\partial L/\partial q_i=Q_i$.