We assume that the forces depend on coordinates and velocities both and are such that they can be derived from a generalized potential \( U \) satisfying $$ \sum_α \vec F_α^{(e)} \frac {\partial \vec r_α} {\partial q_j} = - \frac {\partial U} {\partial q_j} + \frac d {dt} \frac {\partial U} {\partial \dot q_j} \hspace{7em} (33)$$ where \( U \) is a function of \( q, \dot q, t \) Then again (29) can be written in the Lagrangian form. $$ L = \frac d {dt} \left( \frac {\partial L} {\partial \dot q_j} \right) - \frac {\partial L} {\partial q_j} = 0 \hspace{7em} (34) $$ where we again have $$ L = T − U \hspace{7em} (35) $$ We leave verification of (34) as a simple exercise for the reader. \( L \) is called Lagrangian and is a function of generalized coordinates \( q_j \) , generalized velocities \( \dot q_j \) and \(