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The dynamics of a parametrically driven damped pendulum

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Języki publikacji
EN
Abstrakty
EN
Ordered and chaotic states of a parametrically driven planar pendulum with viscous damping are numerically investigated. The damping makes the number of chaotic windows fewer but with larger width. Stroboscopic maps of the chaotic motion of the pendulum, driven either subharmonically or harmonically, show strange attractors with inversion symmetry in the phase plane.
Rocznik
Strony
257--266
Opis fizyczny
Bibliogr. 14 poz., rys., wykr.
Twórcy
autor
  • Department of Mathematics, Jadavpur University Kolkata-700032, INDIA
autor
  • Department of Physics and Meteorology Indian Institute of Technology Kharagpur-721302, INDIA
Bibliografia
  • [1] Arscott F.M. (1964): Periodic Differential Equations. – Pergamon.
  • [2] Baker G.L. and Gollub J.P. (1990): Chaotic Dynamics: an Introduction. – Cambridge University Press.
  • [3] Bartuccelli M.V., Gentile G. and Georgiou K.V. (2001): On the dynamics of a vertically driven damped planar pendulum. – Proc. R. Soc. Lond A, vol.457, pp.3007-3022.
  • [4] Bender C.M. and Orszag S.A. (1978): Advanced Mathematical Methods for Scientists and Engineers. – McGrew Hill.
  • [5] Faraday M. (1831): On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. – Trans. R. Soc. Lond. A, vol.121, pp.299-340.
  • [6] Jing Z. Jing and Yang J. (2006): Complex dynamics in pendulum equation with parametric and external excitations I. – Int. J. Bifurcation and Chaos, vol.16, No.10, pp.2887-2902.
  • [7] Jordan D.W. and Smith P. (1977): Nonlinear Ordinary Differential Equations. – Oxford: Clarendon Press.
  • [8] Kumar K. (1996): Linear theory of faraday instability in viscous liquids. – Proc. R. Soc. A, vol.452, pp.1113-1126.
  • [9] Landau L.D. and Lifschitz E.M. (1976): Mechanics, 3rd edn.. – Oxford: Pergamon.
  • [10] Leven R.W., Pompe B., Wilke C., and Koch B.P. (1985): Experiments on periodic and chaotic motions of a parametrically forced pendulum. – Physica D, vol.16, pp.371-384.
  • [11] McLaughlin J. (1981): Period-doubling bifurcations and chaotic motions for a parametrically forced pendulum. – Journal of Statistical Physics, vol.24, pp.375-388.
  • [12] Starrett J. and Tagg R. (1995): Control of a chaotic parametrically driven pendulum. – Phys. Rev. Lett., vol.74, No.11, pp.1974-1977.
  • [13] Van de Water W., Hoppenbrouwers M., and Christiansen F. (1991): Unstable periodic orbits in the parametrically excited pendulum. – Phys. Rev. A, vol. 44, No.10, pp.6388-6398.
  • [14] Wolf A., Swift J.B., Swinney H.L. and Vastano J.A. (1985): Determining Lyapunov exponents from a time series. – Physica D, vol.16, No.3, pp.285-317.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5793b487-167d-451a-a80e-4959705ba185
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