Whole Body Angular Momentum

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From [5] and [6] of Angular Momentum - Rigid Body, the whole body angular momentum about its CM is the sum of those of the segments about the whole body CM:

[1]

where H_Ri = the remote angular momentum term of segment i, and H_Li = the local angular momentum term. From Figure 1 and [5] and [6] of Angular Momentum - Rigid Body:

Figure 1

[2]

where r_i = the relative position of the segment CM to the whole body CM, v_i = the relative velocity of the segment CM to the whole body CM, I_CMi = the inertia tensor of the segment, and w_i = the angular velocity of the segment.

From [1] and [2]:

[3]

where

[4]

and T_i/G = the transformation matrix from the global frame to frame i, and I_CM = the inertia tensor of the segment about its CM.