How to get the time derivative of jacobian matrix dJc/dt in LOCAL_WORLD_ALIGNED using pinocchio?

[ALICEYZ5]

Hi All,
This question was originally posted in #2141.
I would like to get the time derivative of jacobian matrix in LOCAL_WORLD_ALIGNED, however, as discussing in #2141 , getFrameJacobianTimeVariation returns dJs/dt, which is the time derivative with respect to the spatial acceleration, not dJc/dt. In #2141 , it gives an example of getting dJc/dt in LOCAL. Then, how do we get dJc/dt expressed in LOCAL_WORLD_ALIGNED?
The following code was used:

import pinocchio as pin
import numpy as np

np.set_printoptions(precision=3, suppress=True)

model = pinocchio.buildSampleModelManipulator()
data = model.createData()
frame_idx = model.getFrameId(model.frames[-1].name)

q = np.random.rand((model.nv))
v = np.random.rand((model.nv))
v_dot = np.random.rand((model.nv))

pin.forwardKinematics(model, data, q, v, v_dot)
pin.computeJointJacobiansTimeVariation(model, data, q, v)
pin.updateFramePlacements(model, data)

J_s = pin.getFrameJacobian(model,data,frame_id=frame_idx, reference_frame=pin.LOCAL_WORLD_ALIGNED)
# compute the time derivative of the Jacobian in world frame
Jdot_s = pin.getFrameJacobianTimeVariation(model,data,frame_id=frame_idx, reference_frame=pin.LOCAL_WORLD_ALIGNED)

print(J_s)
print(Jdot_s)

@stephane-caron