Discontinuity-induced bifurcations in a piecewise-smooth capsule system with bidirectional drifts

Discontinuous friction and impact exist in a variety of piecewise-smooth dynamical systems that exhibit rich and complex nonlinear phenomena. This paper aims to study the discontinuity-induced grazing and adding-sliding bifurcations in a piecewise-smooth capsule system subjected to bidirectional drifts. For this purpose, analytical and semi analytical onset conditions of the impact-induced grazing and the friction-induced adding sliding bifurcations are investigated by solving explicitly the underlying piecewise-linear model. In this way, parametric relations revealing the occurrence mechanisms of transitions of the system from stationary to forward progression are derived. This analytical approach is verified numerically using path-following techniques for piecewise-smooth dynamical systems. The numerical investigation includes a parametric study of the observed capsule's average velocity and power consumption suggesting optimum parameters for system operation. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

This paper investigates the discontinuity-induced grazing and adding-sliding bifurcations in a piecewise-smooth capsule system subjected to bidirectional drifts, providing onset conditions and parametric relations through solving the underlying piecewise-linear model. The analytical approach is numerically verified for studying piecewise-smooth dynamical systems, with optimal parameters suggested for system operation based on a parametric study of the observed capsule's average velocity and power consumption.