Dynamics and Bifurcations ofNon - Smooth Mechanical Systems

By Remco I. Leine, H. Nijmeijer. 2006

838 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/eaa976e9c74d27b4258a01af9563c2f6b8bcf81f

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In Civil and Structural Engineering

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Bifurcation phenomena in non-smooth dynamical systems (2006, neutral): “at time instance t p causes the fundamental solution matrix to jump, which we describe by a saltation matrix S (Leine and Nijmeijer, 2004) Φ(t + p , 0, x 0 ) = SΦ(t − p , 0, x 0 ) (19) with S = I + (f + p − f − p )n T n T f − p + ∂h ∂t (t p , x(t p )) (20) where f ± p are the right-hand sides…”
Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques (2009, background): “In principle, systems with nonsmooth nonlinearities can be studied with the proposed method, but they require a special treatment [18].”
Bifurcation and chaos near sliding homoclinics (2010, background): “Many non-smooth models can be found in [1,2, 4,9,19,21,31,32,36,43–45].”
Poincaré maps modeling and local orbital stability analysis of discontinuous piecewise affine periodically driven systems (2007, methodology): “[1–9].”
Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems (2012, methodology): “where the Lebesgue measure is represented by dt and dη represents the sum of the Dirac impulse measures at the impact times [49].”
Bifurcations in Nonsmooth Dynamical Systems (2008, background): “events have in the past been given the name nonsmooth bifurcations [75], discontinuous bifurcations [76, 77], discontinuity-driven bifurcations [30, 109], and, in the Russian literature [49], C-bifurcations.”
Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach (2010, background): “This set of algebraic inclusions can be solved with a linear complementarity problem (LCP) formulation or by an augmented Lagrangian approach (ALA) [17].”
Three crossing limit cycles in planar piecewise linear systems with saddle-focus type (2014, neutral): “2010 Mathematics Subject Classification: 34A36, 34C05, 34C23, 37G05.”