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T. Stachowiak and T. Okada, “A Numerical Analysis of Chaos in the Double Pendulum,” Chaos, Solitons and Fractals, Vol. 29, No. 2, 2006, pp. 417-422.

has been cited by the following article:

• TITLE: Classical and Fractional-Order Analysis of the Free and Forced Double Pendulum

  AUTHORS: Elmas Anli, Ibrahim Ozkol

  KEYWORDS: Double Pendulum, Fractional Dynamics, Lagrangian Dynamics

  JOURNAL NAME: Engineering, Vol.2 No.12, January 10, 2011

  ABSTRACT: This paper presents the fractional-order dynamics of the double pendulum by means of fractional-order modeling. Equations of motion have been derived for cases with and without external forcing. Generalized force terms have been obtained for five different cases of forcing. Both integer and fractional-order analysis have been carried out. Phase diagrams have been plotted to visualize the effect of fractional order approach. The originality of this work arises from the fact that the double pendulum has been modeled with the fractional dynamics approach. The governing equations of motion of the system have been obtained through fractional variational principles.