Advances in Conception about Earthquakes - Earthquake Engineering for Structural Design - page 126

Figure 4.15 Nonlinear behavior and chaos: (a) Changing of periodical fluctuations
in chaotic movements; (b) Periodical fluctuation; (c) Increasing of fluctuation after
bifurcations; (d) Chaotic fluctuations

In the last few decades, physicists became aware that even the system studied
by classical mechanisms can behave in an intrinsically unpredictable manner.
Although such a system may be perfect in principle, its behavior is completely
unpredictable in practice. This phenomenon is called deterministic chaos . To
explain its origin, it is necessary to come to the concept of linear and nonlinear
behavior of systems. Linear equations of equilibrium are easily solved, but the
nonlinear ones are in general very hard or impossible to solve. Therefore, until the
beginning of the 20

th

Century most nonlinear problems in classical mechanics were