Bifurcations of the horizontally forced spherical pendulum

✍ Scribed by P.J. Aston

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 599 KB
• Volume: 170
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(98)00202-3

✦ Synopsis

Various planar motions of the horizontally forced damped spherical pendulum are considered and, in particular, their' stability to non-planar perturbations. By making a careful choice of coordinate.s, all solutions of the planar pendulum can be considered including small amplitude periodic solutions, running oscillations and chaotic solutions. The full nonlinear equations in the chosen coordinates are derived and the symmetries of the system are described. Bifurcation diagrams lbr various types of solutions are presented. Stability of the chaotic solutions is determined by considering a normal Lyapunov exponent.