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Visualization of orbits and pattern evocation for the double spherical pendulum

Marsden, Jerrold E. and Scheurle, Jürgen and Wendlandt, Jeffrey M. (1996) Visualization of orbits and pattern evocation for the double spherical pendulum. In: ICIAM 95 : proceedings of the Third International Congress on Industrial and Applied Mathematics. Mathematical Research. No.87. Akademie Verlag , Berlin, pp. 213-232. ISBN 3055016823 http://resolver.caltech.edu/CaltechAUTHORS:20100923-094959773

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Abstract

This paper explores pattern evocation and the visualization of orbits of the double spherical pendulum. Pattern evocation is a phenomenon where patterns emerge when the ow of a dynamical system is viewed in a frame that rotates relative to the inertial frame. The paper begins with a summary of the theory on pattern evocation for mechanical systems with symmetry. The result of this theory is that if the motion in the reduced space is periodic (respectively, quasiperiodic or almost periodic), then when viewed in a suitably chosen rotating frame with constant velocity, the motion in the unreduced space is periodic (respectively, quasiperiodic or almost periodic). The motion of the system viewed in this rotating frame may have a particular pattern or symmetry. Examples of this theory are demonstrated for the double spherical pendulum. A dierential-algebraic model is created for the double spherical pendulum and is integrated with the simulation package MEXX as well as a custom energy-momentum integrator.


Item Type:Book Section
Additional Information:© 1996, Akademie Verlag. April, 1995; this version: August 2, 1995. Research partially supported by NSF, DOE, and NATO. Research partially supported by DFG and NATO. We thank Michael Dellnitz, Marty Golubitsky, Isaac Kunin, Sergy Prishepionok, and Ian Melbourne for useful comments
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NSFUNSPECIFIED
Department of EnergyUNSPECIFIED
NATOUNSPECIFIED
DFG (Deutsche Forschungsgemeinschaft), GermanyUNSPECIFIED
Record Number:CaltechAUTHORS:20100923-094959773
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100923-094959773
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20096
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Sep 2010 21:05
Last Modified:26 Dec 2012 12:27

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