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American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 482
Probability, pendulums, and pedagogy
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Add to FacebookDeterministic pendula exhibit a spectrum of behavior ranging from periodic to chaotic and provide an opportunity for an introductory discussion on the application of probability techniques to a deterministic system. Analytic and simulation techniques are used to determine probability distributions for a range of dynamical possibilities. In particular, we obtain probability distributions of the pendulum’s angular displacement and distributions of first return times for regular and chaotic motion. For chaotic motion, the latter distribution is modeled by a simple two-state Bernoulli process. Further considerations suggest that not all distributions are probability distributions.
© 2006 American Association of Physics Teachers
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Received Nov 2005
Accepted Feb 2006
Online May 2006
Accepted Feb 2006
Online May 2006
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