a generalized force

The push conjugate to a generalized coordinate. If the coordinate is a length, the generalized force is an ordinary force; if the coordinate is an angle, the generalized force is a torque. It is whatever quantity does work when its corresponding coordinate changes.

It is defined through virtual work: delta W = sum_i Q_i delta q_i, and concretely Q_i = sum_k F_k dot (partial r_k / partial q_i). For forces derivable from a potential, Q_i = -partial V / partial q_i and they fold neatly into the Lagrangian. Forces that do not come from a potential, such as friction or an externally applied drive, enter on the right-hand side of the Euler-Lagrange equation: d/dt (partial L / partial q_dot_i) - partial L / partial q_i = Q_i.

This is precisely how you handle non-conservative or externally applied forces within the Lagrangian framework. Its units are not always newtons: conjugate to an angle, Q has units of torque (newton-meters); conjugate to a charge coordinate, it has units of voltage. What is always guaranteed is that the product Q_i q_i has units of energy.