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The position of the whole body CM can be computed from the positions of the segmental CMs. In Figure 1, let

    Figure 1

    [1]

where i = segment, R_i = the position of the segment CM, R = the position of the whole body CM, and r_i = the relative position of the segment CM to the whole body CM. The sum of the first mass moments of the segments is

    [2]

where M =  the whole body mass. The whole body center of mass is the balance point of the system and must suffice

    [3]

From [2] and [3]:

    [4]

where [x_i, y_i, z_i] = the coordinates of the segment CM.

From [3]:

    [5]

where v_i = the relative velocity of the segment CM to the whole body CM. Therefore:

    [6]

where P = the whole body momentum, and V = the velocity of the whole body CM. As shown in [6], the whole body momentum is the whole body mass times the velocity of the whole body CM. 

© Young-Hoo Kwon, 1998-