Forces are conservative then there exists a function **”*V*”** called potential energy such that $$ \vec F_α^{(e)} = - \vec \nabla_α V \hspace{7em} (25) $$ $$ = - \left( \frac {\partial V} {\partial x_α}, \frac {\partial V} {\partial y_α}, \frac {\partial V} {\partial z_α} \right) \hspace{7em} (26) $$ where \( (x_\alpha, y_\alpha, z_\alpha) \equiv \vec r_\alpha \) are the components of position for the particle \( \alpha \). The generalized force, defined by l.h.s of (22) becomes $$ Q_j = \sum _α \vec F_α . \frac {\partial \vec r_α} {\partial q_j} = - \sum _α \left( \frac {\partial \nu} {\partial x_α} \frac {\partial x_α} {\partial q_j} + \frac {\partial \nu} {\partial y_α} \frac {\partial y_α} {\partial q_j} + \frac {\partial \nu} {\partial z_α} \frac {\partial z_α} {\partial q_j} \right) \hspace{7em} (27) $$ The right-hand side of (27) takes a simple form and $$ \hspace{7em} Q_j = - \frac {\partial V} {\partial q_j} \hspace{7em} (28) $$ Using (28)