Formula_4821

\[\left.\begin{array}{c}m_{v} \ddot{x}_{v}=F_{v x}+\sum_{i=1}^{k} \lambda_{i} \frac{\partial f_{i}}{\partial x_{v}}, \\m_{v} \ddot{y}_{v}=F_{v y}+\sum_{i=1}^{k} \lambda_{i} \frac{\partial f_{i}}{\partial y_{v}}, \\m_{v} \ddot{z}_{v}=F_{v z}+\sum_{i=1}^{k} \lambda_{i} \frac{\partial f_{i}}{\partial z_{v}}, \\v=1,2, \ldots, n,\end{array}\right\} .\]