By selecting different control parameter, the chaotic motion
of the system can be suppressed to different periodic orbits.
Zhang, "Multi-pulse chaotic motions
of high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate," Meccanica, vol.
The Runge-Kutta method is utilized to investigate the bifurcations and chaotic motions
of cracked plate.
19(a)-(d) show spreading, no clear indication appears about nature of chaotic motion
and three-dimensional spreading of the particle path for the cases pointed out above.
produced by resonant forcing is discussed later in the chapter.
For example, chapter 2 explains the notion of fractal intricacy, chapter 6 takes up the "universal" patterns by which systems can go from nonchaotic to chaotic motion
upon parameter variation, chapter 9 explores the senses in which chaotic motion
can be associated with randomness (in the "product" sense) of the dynamical orbits, and chapter 10, directed at the problem of giving a formal definition of a chaotic system, delves more deeply into the basic mathematical structures that lie behind the chaotic results.
All the necessary ingredients for chaotic motion
are present in the equations.
The developed theory is linked to fractals in the sense of Mandelbrot (1983) because truly chaotic motion
often possesses the intricate geometry of the fractal.
The shelves of his office are filled with toys, which he coaxes into chaotic motion
for the entertainment of visitors.
They cover the qualitative analysis of motion in a three-body system, motions of small bodies in the planetary system, the chaotic motion
of orbits, and orbit diffusion.
Nevertheless, a deeper understanding of the bifurcation evolution as well as the transition between stable periodic and chaotic motion
is still essential for designing and adjusting the key parameters to enable the system to perform well.
This talk will present a simplified two dimensional animated model of Hyperion's more complicated full three dimensional motion which, although not capable of showing chaotic motion
(three dimensions are required for chaos in a physical system) does show how a driving torque of Saturn's tidal force functions.