Game Development Reference
In-Depth Information
Rigid-Body Kinematics
The formulas for displacement, velocity, and acceleration discussed in the previous
sections apply equally well for rigid bodies as they do for particles. The difference is that
with rigid bodies, the point on the rigid body that you track, in terms of linear motion,
is the body's center of mass (gravity).
When a rigid body translates with no rotation, all of the particles making up the rigid
body move on parallel paths since the body does not change its shape. Further, when a
rigid body does rotate, it generally rotates about axes that pass through its center of
mass, unless the body is hinged at some other point about which it's forced to rotate.
These facts make the center of mass a convenient point to use to track its linear motion.
This is good news for you since you can use all of the material you learned on particle
kinematics here in your study of rigid-body kinematics.
The procedure for dealing with rigid bodies involves two distinct aspects: 1) tracking
the translation of the body's center of mass, and 2) tracking the body's rotation. The first
aspect is old hat by now—just treat the body as a particle. The second aspect, however,
requires you to consider a few more concepts—namely, local coordinates, angular dis‐
placement, angular velocity, and angular acceleration.
For most of the remainder of this chapter, we'll discuss plane kinematics of rigid bodies.
Plane motion simply means that the body's motion is restricted to a flat plane in space
where the only axis of rotation about which the body can rotate is perpendicular to the
plane. Plane motion is essentially two-dimensional. This allows us to focus on the new
kinematic concepts of angular displacement, velocity, and acceleration without getting
lost in the math required to describe arbitrary rotation in three dimensions.
You might be surprised by how many problems lend themselves to plane kinematic
solutions. For example, in some popular 3D “shoot 'em up” games, your character is able
to push objects, such as boxes and barrels, around on the floor. While the game world
here is three dimensions, these particular objects may be restricted to sliding on the
floor—a plane—and thus can be treated like a 2D problem. Even if the player pushes
on these objects at some angle instead of straight on, you'll be able to simulate the sliding
and rotation of these objects using 2D kinematics (and kinetics) techniques.