Question on jocabian

[xiaosuyang]

The spatial velocity of a rigid body would be the velocitiy of a body-fixed point that coincides with origin O of a frame.So if we use pinocchio::getFrameJacobian(m_model, data, index, pinocchio::LOCAL, J), we will get the $\dot{v}=J\dot{q}$ and the v is ths spatial velocity wrt the LOCAL frame,which is different from the classic velocity of the moving end effector 's frame $\dot{r}_e$. But how to get a classic jocobian wrt the LOCAL frame like the following picture:

[xiaosuyang]

Is the WORLD frame moving with base_link if I use JointModelFreeFlyer to model a floating base robot like biped robot?Is the axis of WORLD frame is same as the base_link's frame ?