Game Development Reference
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Figure 1-10. Transfer of axes
For the simple geometries shown earlier, each coordinate axis represented a plane of
symmetry, and products of inertia go to zero about axes that represent planes of sym‐
metry. You can see this by examining the product of inertia formulas, where, for ex‐
ample, all of the (xy) terms in the integral will be cancelled out by each corresponding
−(xy) term if the body is symmetric about the y-axis, as illustrated in Figure 1-11 .
Figure 1-11. Symmetry
For composite bodies, however, there may not be any planes of symmetry, and the
orientation of the principal axes will not be obvious. Further, you may not even want to
use the principal axes as your local coordinate axes for a given rigid body since it may
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