\sum_{i}p_i\dot{q}_i-\sum_{i}P_i\dot{Q}_i-H+\mathcal{H}=\sum_i\frac{\partial F_1}{\partial q_i}\dot{q}_i +\sum_i\frac{\partial F_1}{\partial Q_i}\dot{Q}_i +\frac{\partial F_1}{\partial t}