Phase diagram for the simple pendulum
This is not the case for the double pendulum in which the bob is at the end of
a jointed pair of rods. If the displacement is small the motion of the double
pendulum is similar to the simple pendulum, but if the displacement is large the
bob swings, rotates, and lurches about and the displacement about the
intermediate joint is seemingly random. If the motion is not forced, the bob will
also come to rest but the curve that describes its motion is far from the well-
behaved spiral of the single pendulum.
Chaotic motion
The characteristic of chaos is that a deterministic system may appear to
generate random behaviour. Let’s look at another example, the repeating, or
iterative, formula a × p × (1 – p) where p stands for the population, measured
as a proportion on a scale from 0 to 1. The value of a must be somewhere
between 0 and 4 to guarantee that the value of p stays in the range from 0 to 1.