Game Development Reference

In-Depth Information

This chapter will primarily discuss the first type of problem, where you know the force(s)

acting on the body, which is more common to in-game physics. The second type of

problem has become important with the advent of motion-based controllers such as the

Sony SixAxis and Nintendo Wii Remote. These controllers rely on
digital accelerome‐

ters
to directly measure the acceleration of a controller. While this is most often used to

find the controller's orientation, it is also possible to integrate the time history of these

sensor values to determine velocity and position. Additionally, if you know the mass of

the controller or device, you can find the force. Accelerometers are found in most

smartphones as well, which also allows for the use of kinematic-based input. So as to

not confuse the two types of problems, we'll discuss the second type, with the acceler‐

ation as input, in detail in
Chapter 21
.

Let us stress that you must consider the sum of
all
of the forces acting on the body when

solving kinetics problems. These include all applied forces and all reaction forces. Aside

from the computational difficulties of solving the equations of motion, one of the more

challenging aspects of kinetics is identifying and properly accounting for all of these

forces. In later chapters, you'll look at specific problems where we'll investigate the

particular forces involved. For now, and for the purpose of generality, let's stick with the

idealized forces introduced in the previous chapter.

Here is the general procedure for solving kinetics problems of interest to us:

1. Calculate the body's mass properties (mass, center of mass, and moment of inertia).

2. Identify and quantify all forces and moments acting on the body.

3. Take the vector sum of all forces and moments.

4. Solve the equations of motion for linear and angular accelerations.

5. Integrate with respect to time to find linear and angular velocity.

6. Integrate again with respect to time to find linear and angular displacement.

This outline makes the solution to kinetics problems seem easier than it actually is

because there are a number of complicating factors that you'll have to overcome. For

example, in many cases the forces acting on a body are functions of displacement, ve‐

locity, or acceleration. This means that you'll have to use iterative techniques in order

to solve the equations of motion. Further, since you most likely will not be able to derive

closed-form solutions for acceleration, you'll have to numerically integrate in order to

estimate velocity and displacement at each instant of time under consideration. These

computational aspects will be addressed further in
Chapter 7
through
Chapter 13
.