Trends in Applications of Mathematics to Mechanics: Proceedings of the 7th Symposium, Held in Wassenaar, The Netherlands, December 711, 1987 [Paperback]

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.I Perturbation Methods and Applications.- Asymptotic Analysis of Stabilizing Fronts.- Boundary Layer Analysis for Some Problems of Singular Domain Perturbation.- Global Behaviour of Very Thin Cellular Structures. Applications to Networks.- Nonlinear Diffusion in Stellar Magnetic Loops.- Perturbation Solutions of Magnetomechanical Signal Processing Devices.- An Asymptotic Theory for a System of Weakly Nonlinear Wave Equations.- II Instability, Bifurcations and Transition to Chaos.- Quasi-Codimension 3 Bifurcation of Invariant T2 Tori for Maps.- Generalized Lieb-Thirring Inequalities and the Dimension of Attractors Associated to the Ginzburg-Landau p.d.e..- Low Order Spectral Models in Hydrodynamics.- Asymptotical Behaviour of Solutions to Quasi-Linear Schr?dinger Equations.- Lyapounov Stability of Electro-Magneto-Elastic Systems.- Criticality of an Exothermic Reaction-Diffusion System of nth-Order.- Flow Induced Bifurcations to Three-Dimensional Motions of Tubes with an Elastic Support.- Local and Global Bifurcations of a Three Particle System.- III Multibody Dynamics and Control.- Multibody System Dynamics Mathematical Theory and Industrial Applications.- A Finite Element Dynamic Analysis of Robotic Manipulators with Flexible Links.- IV Mechanics and Mathematics of Non-Classical Materials.- Mathematical Modelling for Non-Clasl)