Whole Body Center of Mass
Up ] [ Whole Body Center of Mass ] Whole Body Moment of Inertia ] Whole Body Angular Momentum ]

 

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, Ri = the position of the segment CM, R = the position of the whole body CM, and ri = 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 [xi, yi, zi] = the coordinates of the segment CM.

From [3]:

    [5]

where vi = 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-