For smooth dynamical systems, Lyapunov exponents are a well-established tool for making
qualitative predictions about the long-term behaviour of the system, since they describe the …

A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of
continuous-time piecewise-smooth dynamical systems. Motivated by applications, a …

Page 1 LECTURE NOTES IN APPLIED AND COMPUTATIONAL MECHANICS VOL. 43 Raouf A.
Ibrahim Vibro-Impact Dynamics Modeling, Mapping and Applications Springer Page 2 Lecture …

This paper presents a unified framework for performing local analysis of grazing bifurcations
in n-dimensional piecewise-smooth systems of ODEs. These occur when a periodic orbit …

The treatment of ship impacts and collisions takes different approaches depending on the
emphasis of each discipline. For example, dynamicists, physicist, and mathematicians are …

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The
focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting …

Mechanics provides the link between mathematics and practical engineering app-cations. It
is one of the oldest sciences, and many famous scientists have left and will leave their mark …

A rich variety of dynamical scenarios has been shown to occur when a fixed point of a non-
smooth map undergoes a border-collision. This paper concerns a closely related class of …

Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a
variety of “unusual” physical phenomena by means of nonlinear differential equations …

This paper considers dynamical systems that are derived from mechanical systems with
impacts. In particular we will focus on chattering—accumulation of impacts—for which local …