ANALYSIS OF NON-LINEAR DYNAMICS AND BIFURCATIONS OF A DOUBLE PENDULUM

✍ Scribed by P. Yu; Q. Bi

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 642 KB
• Volume: 217
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1781

✦ Synopsis

In this paper, the dynamic behaviour of a double pendulum system in the vicinity of several compound critical points is explored through both analytical and numerical approaches. Four types of critical points are considered, which are characterized by a double zero eigenvalue, a simple zero and a pair of pure imaginary eigenvalues, and two pairs of pure imaginary eigenvalues including resonant and non-resonant cases. With the aid of normal form theory, the explicit expressions for the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. Possible bifurcations leading to 2-D and 3-D tori are also investigated. Closed form stability conditions of the bifurcation solutions are presented. A time integration scheme is used to find the numerical solutions for these bifurcation cases, which agree with the analytic results. Finally, numerical simulation is also applied to obtain double-period cascading bifurcations leading to chaos.