Special Issue: Dynamics of Systems With Impacts

Abstract

In single degreeoffreedom (DOF) oscillators, impacts can occur with a barrier while in a system with multiple DOF, one can additionally observe impacts among interacting bodies. On the one hand, impacts are intrinsic for the operations of many engineering devices. On the other hand, impacts may induce dangerous forces or perturb operations in systems where we expect to have smooth dynamics. In both situations, a deep understanding of the system dynamics can help predict the system behavior and also form a picture of the implications of impacts. Systems experiencing impacts are part of a large group of systems modeled by discontinuous differential equations; their dynamics is also interesting from a theoretical standpoint. Finding accurate numerical solutions of a discontinuous system of equations remains a challenging task in the field of nonlinear dynamics. There are many open problems associated with numerical and analytical investigations of impact oscillators; for example, the current toolboxes for continuation can only be used to determine the bifurcation diagrams for specific types of equations and constraints.