Analysis of the Triple Pendulum as a Hyperchaotic System
A. E. Botha, Guoyuan Qi · 2013
An analysis is made of the hyperchaotic behaviour of a triple plane pen- dulum. It is shown that there are only eight physically distinct equilibrium cong- urations for the pendulum and that the types of eigen solutions obtained, for the Jacobian matrix evaluated at each equilibrium conguration, are independent of the system parameters. A new method for extracting the periodic orbits of the system is also developed. This method makes use of least-squares minimisation and could possibly be applied to other non-linear dynamic systems. As an example of its use, four periodic orbits, two of which are numerically unstable, are found. Time series plots and Poincar e maps are constructed to investigate the periodic to hyperchaotic transition that occurs for each unstable orbit. Keywords: Triple pendulum; hyperchaos; xed points; periodic orbits.