Game Development Reference

In-Depth Information

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