
276 Introduction to Computational Modeling
horizontal displacement of the object is denoted by x. The problem is to find the
instantaneous change in the displacement of the object.
The dynamic behavior of the object is defined by Newton’s law, and is expressed
as follows:
m
d
2
x
dt
2
= F −kv
Because the velocity is the instantaneous change of the displacement, and the
acceleration is the instantaneous change in the velocity of the object, the previous
equation is expressed as follows:
v =
dx
dt
m
dv
dt
= F −kv
For this problem, the two state variables are displacement x, and the velocity
v, of the object. The input variable, u
1
, is the force F. The two state equations ...