Whole Body Moment of Inertia
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The moment of inertia of the whole body about its CM is equal to the sum of those of the individual segments about the whole body CM:

   [1]

where i = segment, and I' = the moment of inertia of a segment with respect to the whole body CM. WB in the equation stands for the whole body reference frame. From [5], [13] & [14] of Transformation of the Inertia Tensor:

   [2]

where

    [3]

    [4]

    [5]

and Ti/WB = the transformation matrix from the whole body frame to the reference frame of segment i, ICMi = the inertia tensor of segment i, mi = the mass of the segment, [x'i, y'i, z'i] = the relative position of the segment CM to the whole body CM, and () = the reference frame of description. Note in [5] it was assumed that the relative coordinates of the segment CM to the whole body CM are described in the WB frame. So no further transformation is required. It was also assumed in [4] that the axes of the segmental reference frames are all principal axes. See Principal Axes for the details of the principal moments of inertia and axes. [2] is useful when one tries to assess the moment of inertia of the body at certain body configuration.

 

Young-Hoo Kwon, 1998-