Game Development Reference

In-Depth Information

F
p
= mg (w/h) - F
f1

Here you can see that the tipping force, applied to the upper edge, is proportional to the

weight and size of the box (actually the ratio of its width to its height), which you can

readily appreciate from a physical point of view. The friction term is important here

because the existence of the friction force actually helps the box to tip. If the box were

on a frictionless surface, it would tend to slide rather than tip.

In the case of plane motion, or 2D motion, of rigid bodies as discussed here, you are

able to readily set up the equations of motion and investigate both the linear as well as

angular motion of the body. In generalized three-dimensional motion, the linear motion

of rigid bodies is no different from that of particles; you simply track the motion of the

rigid body's center of gravity. In three dimensions, however, rotation gives us some grief,

as it is no longer a simple matter of treating rotation about a single axis as in plane

motion. In 3D you'll have to consider rotation about any axis, which leads to some

difficulties in representing arbitrary rotations (Euler angles won't work for us) as well

as to complications with determining moments of inertia for rotation about any axis.

We'll discuss these issues in
Chapter 11
through
Chapter 13
.