Abstract
The planar double pendulum consists of two coupled pendula, i.e. two point masses m 1 and m 2 attached to massless rods of fixed lengths l 1 and l 2 moving in a constant gravitational field (compare Fig. 5.1). For simplicity, only a planar motion of the double pendulum is considered. Such a planar double pendulum is most easily constructed as a mechanical model to demonstrate the complex dynamics of nonlinear (i.e. typical) systems in mechanics, in contrast to the more frequently discussed linear (i.e. atypical) harmonic oscillators. Here, numerical experiments are helpful for investigating the complex dynamics, in particular by means of Poincaré sections.
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References
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, NumericalRecipes (Cambridge University Press, Cambridge 1986)
R. W. Stanley, Numerical methods in mechanics, Am. J. Phys. 52 (1984) 499
T. Shinbrot, C. Grebogi, J. Wisdom, and J. A. Yorke, Chaos in a double pendulum, Am. J. Phys. 60 (1992) 491
P. H. Richter and H.-J. Scholz, Das ebene Doppelpendel — The planar double pendulum, Film C1574, Publ. Wiss. Film., Sekt. Techn. Wiss./Naturw., Ser.9 (1986) Nr. 7/C1574
F. C. Moon, Chaotic Vibrations (John Wiley, New York 1987)
D. R. Stump, Solving classical mechanics problems by numerical integration of Hamilton’s equations, Am. J. Phys. 54 (1986) 1096
R. B. Levien and S. M. Tan, Double pendulum: An experiment in chaos, Am. J. Phys. 61 (1993) 1038
D.J. Tritton, Ordered and chaotic motion of a forced spherical pendulum, Eur. J. Phys. 7 (1986) 162
R. Cuerno, A. F. Rafiada, and J. J. Ruiz-Lorenzo, Deterministic chaos in the elastic pendulum: A simple laboratory for nonlinear dynamics, Am. J. Phys. 60 (1992) 73
K. Briggs, Simple experiments in chaotic dynamics, Am. J. Phys. 55 (1987) 1083
J. A. Blackburn, H. J. T. Smith, and N. Gronbech-Jensen, Stability and Hopf bifurcations in an inverted pendulum, Am. J. Phys. 60 (1992) 903
H. J. T. Smith and J. A. Blackburn, Experimental study of an inverted pendulum, Am. J. Phys. 60 (1992) 909
N. Alessi, C. W. Fischer, and C. G. Gray, Measurement of amplitude jumps and hysteresis in a driven inverted pendulum, Am. J. Phys. 60 (1992) 755
D. Permann and I. Hamilton, Self-similar and erratic transient dynamics for the linearly damped simple pendulum, Am. J. Phys. 60 (1992) 442
Y. Cohen, S. Katz, A. Perez, E. Santo, and R. Yitzak, Stroboscopic views of regular and chaotic orbits, Am. J. Phys. 56 (1988) 1042
E. Marega, Jr., S. C. Zilio, and L. Ioriatti, Electromechanical analog for Landau’s theory of second-order symmetry-breaking transitions, Am. J. Phys. 58 (1990) 655
E. Marega, Jr., L. Ioriatti, and S. C. Zilio, Harmonic generation and chaos in an electromechanical pendulum, Am. J. Phys. 59 (1991) 858
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© 1994 Springer-Verlag Berlin Heidelberg
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Korsch, H.J., Jodl, HJ. (1994). The Double Pendulum. In: Chaos. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02991-6_5
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DOI: https://doi.org/10.1007/978-3-662-02991-6_5
Publisher Name: Springer, Berlin, Heidelberg
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