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

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.