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G.S. Whiston

Bio: G.S. Whiston is an academic researcher. The author has contributed to research in topics: Phase space & Poincaré map. The author has an hindex of 1, co-authored 1 publications receiving 156 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the steady state, vibro-impacting responses of one dimensional, harmonically excited, linear oscillators are studied by using a modern dynamical systems approach allied with numerical simulation.

162 citations


Cited by
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Journal ArticleDOI
TL;DR: In this article, the singularities caused by grazing impact are studied using analytical methods, and it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter, a special type of bifurcation occurs.

711 citations

Journal ArticleDOI
TL;DR: A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems, to explain dynamics that may be observed in simulations of systems which include friction oscillators, impact oscillator, DC-DC converters, and problems in control theory.
Abstract: 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 pragmatic approach is taken to defining a discontinuity-induced bifurcation (DIB) as a nontrivial interaction of a limit set with respect to a codimension-one discontinuity boundary in phase space. Only DIBs that are local are considered, that is, bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows. Three classes of systems are considered, involving either state jumps, jumps in the vector field, or jumps in some derivative of the vector field. A rich array of dynamics are revealed, involving the sudden creation or disappearance of attractors, jumps to chaos, bifurcation diagrams with sharp corners, and cascades of period adding. For each kind of bifurcation identified, where possible, a kind of “normal form” or discontinuity mapping (DM) is given, together with a canonical example and an application. The goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators, impact oscillators, DC-DC converters, and problems in control theory.

342 citations

Journal ArticleDOI
TL;DR: In this article, the main focus is on piecewise smooth systems, which have recently attracted a lot of attention, but also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities.

250 citations

Journal ArticleDOI
TL;DR: In this article, the non-differentiable nature of vibro-impact dynamics can lead to breakdown of the global stable manifold theorem applicable to smooth dynamical systems, and the breakdown leads to the "shredding" of the stable manifolds.

145 citations