Chaotic pendulum: The complete attractor

American Journal of Physics

Volumn 71, Issue 3, 2003, Pages 250-257

  DeSerio, Robert ^a  

^a University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037339359     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1526465     Document Type: Review

References (24)

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4. The Chaotic Pendulum and the Rotary Motion Sensor, Pasco Scientific, 10101 Foothills Blvd., Roseville, CA 95747-7100
5. The PCI-6601 timer/counter board, CB-68LP connector block, and R6868 ribbon cable, National Instruments, 11500 N. Mopac Expwy., Austin, TX 38759-3504 and 〈www.ni.com〉.
6. Our stepper motor system uses a MO61-FD301 Slo-Syn stepper motor (Servo Systems, Co., 115 Main Rd., Montville, NJ 07045-0097 and 〈www.servosystems.com〉) and an Allegro 5804 BiMOS II Unipolar Stepper-Motor Translator/Driver, Allegro MicroSystems, Inc., 115 Northeast Cutoff, Worcester, MA 01606 and 〈www.allegromicro.com〉.
7. The LabVIEW programming language, National Instruments, 11500 N. Mopac Expwy., Austin, TX 38759-3504 and 〈www.ni.com〉.
8. The University of Florida Advanced Physics Laboratory web site is at 〈www.phys.ufl.edu/courses/phy4803L〉.
9. The TISEAN nonlinear time series analysis package can be found at 〈www.mpipks-dresden.mpg.de/̃tisean〉.
10. The gnuplot plotting software web site is at 〈www.gnuplot.info〉.
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13. There are small corrections to d = A cos φ that depend on the drive amplitude A and the distance from the motor shaft to the guide hole (60 cm for our setup). For the largest drive amplitude used (A = 6 cm), there will be a 0.15 cm downward shift in the midpoint of the oscillation (from its value for A = 0) and an additional cos 2φ term of amplitude 0.15 cm.
14. G. L. Baker, J. P. Gollub, and J. A. Blackburn, "Inverting chaos: extracting system parameters from experimental data," Chaos 6, 528-533 (1996).
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17. F(u) would also depend on the drive phase φ, and for small enough τ would be given by F(u) = u+ τG(u) where the θ and Ω components of G are the right-hand sides of Eqs. (2a) and (2b), respectively.
18. Reggie Brown, Paul Bryant, and Henry D. I. Abarbanel, "Computing the Lyapunov spectrum of a dynamical system from an observed time series," Phys. Rev. A 43, 2787-2806 (1991).
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24. G. L. Baker and J. P. Gollub, Chaotic Dynamics: An Introduction, 2nd ed. (Cambridge U.P., Cambridge, 1996), Chap. 6.