How to obtain centroidal momentum matrix explicitly for momentum-based control purpose

Question

there are useful APIs to calc centroidal momentum, like CalcSpatialMomentumInWorldAboutPoint. But for momentum-based control, I ran into some problems with this API. During control there is:

l = A(q) * v

and I want to take this as a constraint to solve vdot (joint accelerations)

l_dot = A(q) * vdot + Adot(q) * v 

where l is the stacked vector of linear and angular momentum, A(q) is the centroidal momentum matrix.

My questions are:

1. Is there any method to get the centroidal momentum matrix explicitly?
2. Currently drake use CalcBiasCenterOfMassTranslationalAcceleration to get the translational part of Adot(q) * v, can we get the rotational part too?

@hongkai-dai discussed this at here, it is also mentioned in other literature [1][2]. Thanks very much for any suggestions.

[1] Koolen, Twan, et al. "Design of a momentum-based control framework and application to the humanoid robot atlas." International Journal of Humanoid Robotics 13.01 (2016): 1650007.
[2] Lee, Sung-Hee, and Ambarish Goswami. "A momentum-based balance controller for humanoid robots on non-level and non-stationary ground." Autonomous Robots 33.4 (2012): 399-414.