The tuning conditions for circular, cycloidal and epicycloidal centrifugal pendula: A unified cartesian approach

In this paper, the methodology of Desoyer and Slibar, for an approximate analytical solution of the nonlinear differential equations governing the dynamics of a circular centrifugal pendulum, has been herein extended to the case of cycloidal and epicycloidal pendula paths. Another distinctive feature treatment of this investigation is the use of parametric cartesian equations of the mass pendulum for the cycloidal and epicycloidal paths. The tuning conditions for the three cases of circular, cycloidal and epicycloidal centrifugal pendula have been deduced. These are consistent with the findings of Denman. Due to the tautochronism associated with these paths, the centrifugal pendula with such paths demonstrated a damping capabilities also under large oscillations. The numerical examples discussed confirm such features. (C) 2020 Elsevier Ltd. All rights reserved.