Complex sentence: Since we are free to specify the initial values of the generalized coordinates and velocities separately, the generalized coordinates "q j" and velocities "dq j"/ "dt" can be treated as "independent variables".
Split into simpler sentences: Since we are free to specify the initial values of the generalized coordinates and velocities separately, the generalized coordinates and velocities can be treated as independent variables. The generalized coordinates "q j" and velocities "dq j"/ "dt" are treated as "independent variables".