Ebook: 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.

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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.

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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.
Content:
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 T2 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 Schr?dinger Equations....Pages 98-107
Lyapounov Stability of Electro-Magneto-Elastic Systems....Pages 108-118
Criticality of an Exothermic Reaction-Diffusion System of nth-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
Mathematical Aspects of the Theory of Viscoelasticity....Pages 224-237
Front Matter....Pages 238-250
On Saint-Venant’s Problem and Saint-Venant’s Principle in Nonlinear Elasticity....Pages 251-251
Hypermembrane Shells....Pages 252-260
On the Problem of Constructing the Mathematical Theory of Plates and Shells....Pages 261-272
Application of Extremum Principles to Mixed Boundary-Value Problems in Non-linear Elasticity....Pages 273-279
Application of Bivariate B-Splines to a Plate Bending Problem....Pages 280-289
Entropy and Dynamical Stability — a Method Due to Lagrange-Formalism as Applied to Thermodynamics of Irreversible Processes....Pages 290-296
A Thermodynamic Theory for Turbulence....Pages 297-320
Approach to Lower Dimensional Dynamical Systems: Thermodynamical Aspects....Pages 321-328
A Functional Analytic Approach to an Optimization Problem of Hydrodynamic Propulsion....Pages 329-341
Nonlinear Problems in the Kinetic Theory of Gases....Pages 342-350
Back Matter....Pages 351-360
....Pages 361-361