Analysis of the Triple Pendulum as a Hyperchaotic System
نویسندگان
چکیده
An analysis is made of the hyperchaotic behaviour of a triple plane pendulum. It is shown that there are only eight physically distinct equilibrium configurations for the pendulum and that the types of eigen solutions obtained, for the Jacobian matrix evaluated at each equilibrium configuration, 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 Poincaré maps are constructed to investigate the periodic to hyperchaotic transition that occurs for each unstable orbit.
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