Editing Controllability (section)

===Analogy for example of ''n'' = 2===
Consider an [[Car analogy|analogy]] to the previous example system.
You are sitting in your car on an infinite, flat plane and facing north.
The goal is to reach any point in the plane by driving a distance in a straight line, come to a full stop, turn, and driving another distance, again, in a straight line.
If your car has no steering then you can only drive straight, which means you can only drive on a line (in this case the north-south line since you started facing north).
The lack of steering case would be analogous to when the rank of <math>C</math> is 1 (the two distances you drove are on the same line).

Now, if your car did have steering then you could easily drive to any point in the plane and this would be the analogous case to when the rank of <math>C</math> is 2.

If you change this example to <math>n=3</math> then the analogy would be flying in space to reach any position in 3D space (ignoring the [[Orientation (rigid body)|orientation]] of the [[aircraft]]).
You are allowed to:
*fly in a straight line
*turn left or right by any amount ([[Yaw (flight)|Yaw]])
*direct the plane upwards or downwards by any amount ([[Pitch (flight)|Pitch]])
Although the 3-dimensional case is harder to visualize, the concept of controllability is still analogous.