Transcription of School of Physics, University of Sydney, NSW 2006, …
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School of Physics, University of Sydney, NSW 2006, …
The following article has been accepted by the American Journal of Physics. After it is published, it will be found at of a double pendulum with distributed massM. Z. Rafat, M. S. Wheatland, and T. R. Bedding School of Physics, University of Sydney, NSW 2006, AustraliaAbstractWe investigate a variation of the simple double pendulum in which the two point masses arereplaced by square plates. The double square pendulum exhibits richer behavior than the simpledouble pendulum and provides a convenient demonstration of nonlinear dynamics and chaos. Itis also an example of an asymmetric compound double pendulum, which has not been studied indetail. We obtain the equilibrium configurations and normal modes of oscillation and derive theequations of motion, which are solved numerically to produce Poincar e sections. We show how thebehavior varies from regular motion at low energies, to chaos at intermediate energies, and backto regular motion at high energies.
not lie along the line joining the two axles. In this regard it is closest to the asymmetri-cal double pendulum studied in Ref. 8, although that pendulum does not have distributed
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