Abstract: In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.
Abstract: This paper numerically investigates the effects of input
speed on the overall dynamic characteristics of a multi-body system
with differently located revolute clearance joints without friction. A
typical planar slider-crank mechanism is used as a demonstration case
in which the effects of the input speed on the dynamic performance
of the mechanism with a revolute clearance joint between the crank
and connecting rod, and between the connecting rod and slider are
separately investigated with comprehensive observations numerically
presented. It is observed that, changing the driving speed of a multibody
system makes the behavior of the system to change from
either periodic to chaotic, or chaotic to periodic depending on which
joint has clearance. The location of the clearance revolute joint and
the operating speed of a multi-body system play a crucial role in
predicting accurately the dynamic responses of the system. Therefore
the dynamic behavior of one clearance revolute joint cannot be used
as a general case for a mechanical system.