Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 557

Section 12.3. Typically in digital simulations impulsive forces are handled
differently from more persistent forces that act over several simulation steps,
so for now, don't think of a force as an impact; instead, think of it as more
of a gradual push or pull that could be provided by, for example, a spring,
the wind, or gravity.
We said that Equation (12.1) is the traditional way to express the rela-
tionship among force, mass, and acceleration. However, written in that way,
with force on the left-hand side, you might get the idea that the common
situation is for us to know the mass and acceleration, and use Newton's
laws to compute the force. In fact, especially in digital simulations, the
more common scenario is that we have calculated the forces acting on a
body, and we wish to predict the body's response to those forces. In other
words, we'll usually use Newton's second law in the form

We usually use this form
of Newton's second law

a = f /m. (12.2)

Most physics textbooks teach the important conceptual tool known as
a free-body diagram. Newton's second law, especially as expressed in Equa-
tion (12.2), is at the heart of this exercise. The basic procedure is as follows,
starting with a representation of the object.

1. Draw and label all the forces acting on it.

2. Sum up those forces (using vector addition) to compute the net force.

3. Use Newton's second law (Equation (12.2)) to compute the accelera-
tion of the object.

4. Integrate the acceleration to determine the motion of the object.
When solving problems analytically, this means solving differential
equations. We don't use any differential equations in this topic be-
cause there are only a few simple cases that we will look at analyt-
ically. Numerical methods of integration must be used. Later, we
examine Euler integration, which is the most simple method imagin-
able, but also the one used by most real-time rigid body simulators.

The above procedure is a very important tool that we use several times
in Section 12.2; it's also essentially how most digital physics simulations
work inside a computer. Of course, the simplicity with which we've de-
scribed this 4-step process hides many troublesome di culties. The forces
in Equation (12.2) may vary continuously over time; be dependent on time,
position, and velocity; exhibit nonlinearities or discontinuities; and in gen-
eral be di cult to compute exactly or express and integrate in closed form.
Section 12.6 deals with physics simulations, but for now the key point that
we want to emphasize is that Newton's second law is the fundamental driv-
ing equation.