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SUMMARY:Optimised Hyperchaotic Modes of a Triple Pendulum
DTSTART;VALUE=DATE-TIME:20110715T064500Z
DTEND;VALUE=DATE-TIME:20110715T070000Z
DTSTAMP;VALUE=DATE-TIME:20240617T220445Z
UID:indico-contribution-4917@events.saip.org.za
DESCRIPTION:Speakers: André Botha (Unisa)\nAnalytical equations of motion
\, in the form dxi ⁄ dt = fi(x\,t)\, are derived for a damped harmonical
ly driven triple plane pendulum. This form of the equations clearly displa
ys the nature of the non-linear coupling and provides a basis for physical
interpretation. The equations also facilitate the derivation of the Jacob
ian matrix in analytical form\, a result which is important for the accura
te numerical computation of the Lyapunov exponents. It is shown that sets
of optimised parameters\, such as the lengths and masses of the pendulum\,
may be derived by using the Nelder-Mead simplex optimisation algorithm. T
his method gives precise control over the Lyapunov exponents and may be us
eful in a wide variety of other non-linear applications\, such as those oc
curring in biophysics and information technology (for secure communication
). As an example of the technique it is used to predict periodic and quasi
-periodic orbits of the un-damped pendulum\, as well as its chaotic and hy
perchaotic modes. The maximum positive Lyapunov exponents for the pendulum
are found to vary from zero\, for periodic orbits\, to as high as ten for
the optimised hyperchaotic modes. Numerical simulations\, coded in Python
\, are used to visualise the results. \n\nhttps://events.saip.org.za/event
/7/contributions/4917/
LOCATION: Acro5
URL:https://events.saip.org.za/event/7/contributions/4917/
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