Trends in Applications of Mathematics to Mechanics : Proceedings of the 7th Symposium, Held in Wassenaar, The Netherlands, December 7–11, 1987

In many areas of mechanics the interplay between mathematics and physics is crucial for understanding not only underlying principles but also practical applications. This is particularly the case in hydrodynamics and elasticity. Over thirty articles in this volume discuss various aspects including perturbation methods and applications, instability, bifurcations and transition to chaos, multibody dynamics and control, mechanics and mathematics of non-classical materials, and new interactions of mathematics and mechanics. The book addresses scientists and engineers working in these areas including those interested in applied mathematical analysis. Front Matter....Pages I-IX Front Matter....Pages 1-1 Asymptotic Analysis of Stabilizing Fronts....Pages 2-16 Boundary Layer Analysis for Some Problems of Singular Domain Perturbation....Pages 17-25 Global Behaviour of Very Thin Cellular Structures. Applications to Networks....Pages 26-34 Nonlinear Diffusion in Stellar Magnetic Loops....Pages 35-43 Perturbation Solutions of Magnetomechanical Signal Processing Devices....Pages 44-52 An Asymptotic Theory for a System of Weakly Nonlinear Wave Equations....Pages 53-61 Front Matter....Pages 63-63 Quasi-Codimension 3 Bifurcation of Invariant T 2 Tori for Maps....Pages 64-78 Generalized Lieb-Thirring Inequalities and the Dimension of Attractors Associated to the Ginzburg-Landau p.d.e.....Pages 79-85 Low Order Spectral Models in Hydrodynamics....Pages 86-97 Asymptotical Behaviour of Solutions to Quasi-Linear Schrödinger Equations....Pages 98-107 Lyapounov Stability of Electro-Magneto-Elastic Systems....Pages 108-118 Criticality of an Exothermic Reaction-Diffusion System of n th -Order....Pages 119-127 Flow Induced Bifurcations to Three-Dimensional Motions of Tubes with an Elastic Support....Pages 128-138 Local and Global Bifurcations of a Three Particle System....Pages 139-146 Front Matter....Pages 147-147 Multibody System Dynamics Mathematical Theory and Industrial Applications....Pages 148-159 A Finite Element Dynamic Analysis of Robotic Manipulators with Flexible Links....Pages 160-171 Front Matter....Pages 173-173 Mathematical Modelling for Non-Classical Materials....Pages 174-185 Nonstandard Modelling of Certain Quasi-Stationary Debonding Processes in Laminates....Pages 186-192 Multilevel Model of Micro-Macro Interactions and Residual Stresses in Physical Systems....Pages 193-203 Hemivariational Inequalities and Their Applications to Composite Material Structures....Pages 204-214 Front Matter....Pages 173-173 Poiseuille Flows of Incompressible Simple Fluids....Pages 215-223 Properly Posed Boundary Condition and the Existence Theorem for Supefluid He 4 ....Pages 224-237 Mathematical Aspects of the Theory of Viscoelasticity....Pages 238-250 Front Matter....Pages 251-251 On Saint-Venant’s Problem and Saint-Venant’s Principle in Nonlinear Elasticity....Pages 252-260 Hypermembrane Shells....Pages 261-272 On the Problem of Constructing the Mathematical Theory of Plates and Shells....Pages 273-279 Application of Extremum Principles to Mixed Boundary-Value Problems in Non-linear Elasticity....Pages 280-289 Application of Bivariate B-Splines to a Plate Bending Problem....Pages 290-296 Entropy and Dynamical Stability — a Method Due to Lagrange-Formalism as Applied to Thermodynamics of Irreversible Processes....Pages 297-320 A Thermodynamic Theory for Turbulence....Pages 321-328 Approach to Lower Dimensional Dynamical Systems: Thermodynamical Aspects....Pages 329-341 A Functional Analytic Approach to an Optimization Problem of Hydrodynamic Propulsion....Pages 342-350 Nonlinear Problems in the Kinetic Theory of Gases....Pages 351-360 Back Matter....Pages 361-361 Perturbation Methods and Applications Instability, Bifurcations and Transition to Chaos Multibody Dynamics and Control Mechanics and Mathematics of Non-Classical Materials New Interactions of Mathematics and Mechanics Index of Contributors.