An experimental investigation into the dynamics of a string

American Journal of Physics

Volumn 72, Issue 9, 2004, Pages 1157-1169

  Molteno, Timothy C ^a   Tufillaro, Nicholas B ^b  

^a UNIVERSITY OF OTAGO   (New Zealand)

^b NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4544367831     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1764557     Document Type: Article

References (41)

1. J. B. Keller, "Large amplitude motion of a string," Am. J. Phys. 27, 584-586 (1959).
2. P. Morse, Vibrations and Sound, 2nd ed. (McGraw-Hill, Boston, MA, 1936).
3. J. A. Elliott, "Intrinsic nonlinear effects in vibrating strings," Am. J. Phys. 48, 478-480 (1980); "Nonlinear resonance in vibrating strings," ibid. 50, 1148-1150 (1982).
4. J. A. Elliott, "Intrinsic nonlinear effects in vibrating strings," Am. J. Phys. 48, 478-480 (1980); "Nonlinear resonance in vibrating strings," ibid. 50, 1148-1150 (1982).
5. N. B. Tufillaro, "Nonlinear and chaotic string vibrations," Am. J. Phys. 57, 408-414 (1989).
6. J. Johnson and A. Bajaj, "Amplitude modulated and chaotic dynamics in resonant motion of strings," J. Sound Vib. 128, 87-107 (1989).
7. A. Bajaj and J. Johnson, "On the amplitude dynamics and crsis in resonant motion of stretched strings," Philos. Trans. R. Soc. London, Ser. A 338, 1-41 (1992).
8. O. O'Reilly and P. Holmes, "Non-linear, non-planar and non-periodic vibrations of a string," J. Sound Vib. 153, 413-435 (1992).
9. O. O'Reilly, "Global bifurcations in the forced vibrations of a damped string," Int. J. Non-Linear Mech. 28, 337-351 (1993).
10. T. Molteno and N. Tufillaro, "Torus doubling and chaotic string vibrations: Experimental results," J. Sound Vib. 137, 327-330 (1990).
11. T. C. A. Molteno, "Chaos and crisis in strings," Ph.D. thesis, University of Otago, Dunedin, New Zealand, 1994.
12. R. J. Hanson, J. M. Anderson, and H. K. Macomber, "Measurements of nonlinear effects in a driven vibrating-wire," J. Acoust. Soc. Am. 96, 1549-1556 (1994).
13. N. Tufillaro, T. Abbott, and J. Reilly, An Experimental Approach to Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, MA, 1992).
14. S. Strogatz, Nonlinear Dynamics and Chaos (Addition-Wesley, Reading, MA, 1994).
15. R. C. Hilborn and N. B. Tufillaro, "Resource letter: ND-1: nonlinear dynamics," Am. J. Phys. 65, 822-834 (1997).
16. J. E. Berger and G. Nunes, "A mechanical Duffing oscillator for undergraduate laboratory," Am. J. Phys. 65, 841-846 (1997).
17. B. K. Jones and G. Trefan, "The Duffing oscillator: A precise electronic analog chaos demonstrator for the undergraduate laboratory," Am. J. Phys. 69, 464-469 (2001).
18. N. Sungar, J. P. Sharpe, M. J. Moelter, N. Fleishon, K. Morrision, J. Mc-Dill, and R. Schoonover, "A laboratory-based nonlinear dynamics course for science and engineering students," Am. J. Phys. 69, 591-597 (2001).
19. R. Narasihma, "Non-linear vibration of an elastic string," J. Sound Vib. 8, 134-146 (1968).
20. J. Miles, "Resonant, nonplanar motion of a stetched string," J. Acoust. Soc. Am. 75, 1505-1010 (1984).
21. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, NY, 1983).
22. K. Judd and A. Mees, "Modeling chaotic motions of a string from experimental data," Physica D 92, 221-236 (1996).
23. R. Gilmore and M. Lefranc, The Topology of Chaos (Wiley-Interscience, New York, NY, 2002).
24. C. Grebogi, E. Ott, and J. Yorke, "Crises, sudden changes in chaotic attractors and transient chaos," Physica D 7, 181-200 (1983).
25. R. Hanson, "Optoelectronic detection of string vibration," Phys. Teach. (March 1987), 165-166.
26. J. Brundell and T. Molteno, Radioscientist 5, 124 (1994).
27. D. M. Walker, N. B. Tufillaro, and P. Gross, "Radial-basis models for feedback systems with fading memory," IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 1147-1151 (2001).
28. L. Barford, N. Tufillaro, D. Usikov, L. Marochnik, and R. McCutcheon, "Calibration of Hubble space telescope focal-length variations using the emedding technique," Flight Mechanics Symposium (NASA), edited by John P. Lynch, Goddard Space Flight Center, Greenbelt, Maryland, June 19-21 2001, pp. 485-495.
29. E. Knobloch and N. Weiss, "Bifurcations in a model of magneto-convection," Physica D 9, 379-407 (1983).
30. T. Molteno, "A fast O(n) box-counting algorithm for estimating dimensions," Phys. Rev. E 48, 3263-3266 (1993).
31. J. Miles, "Damped spherical pendulum," J. Sound Vib. 140, 327-330 (1993).
32. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, U.K., 1993).
33. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, U.K., 1997).
34. R. Brown, N. Rulkov, and N. Tufillaro, "Synchronization of chaotic Systems - the effects of additive noise and drift in the dynamics of the driving," Phys. Rev. E 50, 4488-4508 (1994).
35. N. B. Tufillaro, P. Wyckoff, R. Brown, T. Schreiber, and T. Molteno, "Topological time series analysis of a string experiment and its synchronized model," Phys. Rev. E 51, 164-174 (1995).
36. D. M. Walker and A. Mees, "Reconstructing nonlinear dynamics by extended Kalman filtering," Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 557-569 (1998).
37. R. Gilmore, "Topological analysis of chaotic systems," Rev. Mod. Phys. 70, 1455-1529 (1998).
38. D. Allingham, M. West, and A. I. Mees, "Wavelet reconstruction of nonlinear dynamics," Chaos 8, 2191-2201 (1998).
39. R. Hegger, H. Kantz, and T. Schreiber, "Practical implementation of nonlinear time series methods: The TISEAN package," Chaos 9, 413-435 (1999).
40. K. Judd and M. Small, "Towards long-term prediction," Physica D 136, 31-44 (2000).
41. M. Small, K. Judd, and A. Mees, "Modeling continuous processes from data," Phys. Rev. E 65, 046704 (2002).