The Dynamics of a Parametrically Driven Damped Pendulum

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.

REFERENCES (14)

Arscott F.M. (1964): Periodic Differential Equations. - Pergamon.

Google Scholar

Baker G.L. and Gollub J.P. (1990): Chaotic Dynamics: an Introduction. - Cambridge University Press.

Google Scholar

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.

Google Scholar

Bender C.M. and Orszag S.A. (1978): Advanced Mathematical Methods for Scientists and Engineers. - McGrew Hill.

Google Scholar

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.

Google Scholar

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.

Google Scholar

Jordan D.W. and Smith P. (1977): Nonlinear Ordinary Differential Equations. - Oxford: Clarendon Press.

Google Scholar

Kumar K. (1996): Linear theory of faraday instability in viscous liquids. - Proc. R. Soc. A, vol.452, pp.1113-1126.

Google Scholar

Landau L.D. and Lifschitz E.M. (1976): Mechanics, 3rd edn.. - Oxford: Pergamon.

Google Scholar

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.

Google Scholar

11.

McLaughlin J. (1981): Period-doubling bifurcations and chaotic motions for a parametrically forced pendulum. - Journal of Statistical Physics, vol.24, pp.375-388.

Google Scholar

12.

Starrett J. and Tagg R. (1995): Control of a chaotic parametrically driven pendulum. - Phys. Rev. Lett., vol.74, No.11, pp.1974-1977.

Google Scholar

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.

Google Scholar

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.

Google Scholar

Submit your paper

eISSN:	2353-9003
ISSN:	1734-4492