Formula_7920

\[\begin{gathered}f_{k}=\sum_{i=1}^{N}\left(a_{k i} \dot{x}_{i}+b_{k i} \dot{y}_{i}+c_{k i} \dot{z}_{i}\right)+d_{k}=0, \\k=1,2, \ldots, r,\end{gathered}\]