IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics

1. Front Matter

   Pages i-xiv

   PDF

2. Analysis Tools, Bifurcation Theory

   1. Front Matter

      Pages 1-1

      PDF

   2. Bifurcation in Stochastically Perturbed Dynamical Systems

      • S. T. Ariaratnam

      Pages 3-11

   3. Nonstationary Responses in Two Degree-of-Freedom Nonlinear Systems with 1-to-2 Internal Resonance

      • Anil K. Bajaj, Bappaditya Banerjee, Patricia Davies

      Pages 13-22

   4. Sinusoidally Varying Period-Doubling Bifurcations

      • Huw G. Davies

      Pages 23-29

   5. Wavelet Approach to Mechanical Problems. Symplectic Group, Symplectic Topology and Symplectic Scales

      • A. N. Fedorova, M. G. Zeitlin

      Pages 31-40

   6. On the Generalized Cell Mapping

      • R. Guder, E. Kreuzer

      Pages 41-50

   7. Bursts

      • Edgar Knobloch, Jeff Moehlis

      Pages 51-60

   8. Dynamics of a Quasiperiodically-Forced Mathieu Oscillator

      • Richard Rand, Randolph Zounes, Rachel Hastings

      Pages 61-70

   9. Improved Galerkin Method in the Dimension Reduction of Nonlinear Dynamical Systems

      • Alois Steindl, Hans Troger, Josef V. Zemann

      Pages 71-80

   10. Sequences of Global Bifurcations and Multiple Chaotic Transients in a Mechanical Driven Oscillator

       • W. Szemplińska-Stupnicka, E. Tyrkiel

       Pages 81-91

   11. Bifurcation of Homoclinic Orbits in Autonomous Systems and in Chaotic Blue Sky Catastrophe

       • M. Belhaq, F. Lakrad

       Pages 93-100

   12. Wavelet Approach to Polynomial Mechanical Problems

       • A. N. Fedorova, M. G. Zeitlin

       Pages 101-108

   13. Jumps to Resonance Phenomena in Nonlinear Mechanics: Fractal Basins, Chaotic Transients and Unpredictability

       • Mohamed S. Soliman

       Pages 109-115

   14. Global Stable Oscillations Near Unstable Equilibrium Positions: The Hilltop Effect

       • M. Zakrzhevsky

       Pages 117-124

3. Elastica, Cables and Shell Dynamics

   1. Front Matter

      Pages 125-125

      PDF

   2. Homoclinic Orbits, Spatial Chaos and Localized Buckling

      • J. M. T. Thompson, G. H. M. Van Der Heijden

      Pages 127-138

   3. Nonregular Regimes of Monodimensional Mechanical Systems with Initial Curvature: Experiments and Time Series Analysis

      • F. Benedettini, G. Rega

      Pages 139-148

   4. Constrained Euler Buckling: Line Contact Solutions

      • Philip Holmes, John Schmitt, Gabor Domokos

      Pages 149-158

   5. The Role of Homoclinic Bifurcations in Understanding the Buckling of Long Thin Cylindrical Shells

      • G. J. Lord, A. R. Champneys, G. W. Hunt

      Pages 159-168

It is two decades since Mitchell Feigenbaum's landmark papers on period doubling and the modern beginnings of what is now called "Chaos Theory". From the very beginning, mechanics has been a central focus for modem nonlinear dynamical systems. Fluid, structural, machine and rigid body dynamics has been a fertile field for nonlinear phenomena and chaos in particular. Early experimental evidence for chaotic phenomena in mechanics gave the new chaos theory a mark of credibility, importance, and relevance that its earlier sister field, catastrophe theory, did not achieve. The fact that mechanics straddles both physics and engineering also meant that mechanics became a pathway for direct application of chaos theory to applied problems. So what is new in nonlinear dynamics and mechanics today? First the scope of applications in solid mechanics has broadened to cover material processing, inelasticity and fracture mechanics. In rigid body dynamics, more complex systems such as vehicles, robotics and controlled machines have come into the purview of nonlinear dynamicists. On the mathematics side of nonlinear dynamics, it is now recognized that spatio-temporal problems, hysteretic and time delay problems are the new frontiers in this field. Also the term "complexity" has been added to the lexicon of chaos theory to describe the dynamics of many interacting sub systems which can exhibit self organization and evolution. Complexity analysis has gained a foothold in biological and some social sciences as well in fluid and chemical physics.

• bifurcation theory
• chaos
• mechanics
• nonlinear dynamics
• solids
• vehicle dynamics

• College of Engineering, Cornell University, Ithaca, USA

  Francis C. Moon

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