Experimental study of regular and chaotic transients in a non-smooth system

This paper focuses on thoroughly exploring the finite-time transient behaviors occurring in a periodically driven non-smooth  dynamical system . Prior to settling down into a long-term behavior, such as a periodic  forced oscillation , or a chaotic attractor, responses may exhibit a variety of transient behaviors involving regular dynamics, co-existing attractors, and super-persistent chaotic transients. A simple and fundamental impacting  mechanical system  is used to demonstrate generic transient behavior in an experimental setting for a single degree of freedom non-smooth  mechanical oscillator . Specifically, we consider a horizontally driven rigid-arm  pendulum system  that impacts an inclined rigid barrier. The forcing frequency of the horizontal oscillations is used as a bifurcation parameter. An important feature of this study is the systematic generation of generic experimental initial conditions, allowing a more thorough investigation of basins of attraction when multiple attractors are present. This approach also yields a perspective on some sensitive features associated with grazing bifurcations. In particular, super-persistent chaotic transients lasting much longer than the conventional settling time (associated with linear viscous damping) are characterized and distinguished from regular dynamics for the first time in an experimental mechanical system.