Advances in Conception about Earthquakes - Earthquake Engineering for Structural Design - page 127

linearly approximated. Linearity basically means that the effects are proportional to
the cause. Contrary, the essence of nonlinearity is that the effects are not
proportional to the cause. Small causes may have large effects. The processes
which are very sensitive to small fluctuations are called chaotic. This is because
their behavior is in general very irregular, so that they give the impression of being
random, even though they are driven by deterministic forces (Heylighen, 2002).
A very illustrative model for this deterministic chaos of dynamical systems is
the nonlinear behavior of a double pendulum (Fig. 4.16a). In horology, a double
pendulum is a system of two pendulums on a common mounting which move in
anti-phase (Wikipedia, nd). The motion of a double pendulum is governed by a set
of coupled ordinary differential equations. Above certain energy, its motion is
changed. The pendulum behavior for small oscillations is very well known. But in
the field of nonlinear behavior, for large oscillations, the motions are chaotic (Fig.
4.16b) (Weisstein, 2007, Wikipedia, nd). The most important result obtained from
(a)
(b)
Figure4.16 Double pendulum behavior (after Weisstein, 2007)