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".
The generalized coordinates "q j" and velocities "dq j"/ "dt" can be treated as "independent variables". We are free to specify the initial values of the generalized coordinates separately. We are free to specify the initial values of velocities separately.