The application of centre manifolds to amplitude expansions. II. Infinite dimensional problems

AbstractThe theory of centre manifolds for infinite dimensional systems is described, with emphasis on the practical computational aspects of applying the theory to near-critical problems, and in particular to computation of the centre manifold. The calculations are illustrated by detailed analyses of two specific problems

The application of centre manifolds to amplitude expansions. I. Ordinary differential equations

AbstractThe theory of centre manifolds for a system of ordinary differential equations is summarized and its relationship to amplitude expansions based upon multiple time scales is discussed. Emphasis is placed upon the practical computational aspects of applying centre manifold theory to near-critical problems, and, in particular, to the computation of the centre manifold. The calculations are illustrated by a detailed analysis of two problems in fluid mechanics

The theory of pseudo-rigid bodies

This monograph concerns the development, analysis, and application of the theory of pseudo-rigid bodies. It collects together our work on that subject over the last five years. While some results have appeared else­ where, much of the work is new. Our objective in writing this mono­ graph has been to present a new theory of the deformation of bodies, one that has not only a firm theoretical basis, but also the simplicity to serve as an effective tool in practical problems. Consequently, the main body of the treatise is a multifaceted development of the theory, from foundations to explicit solutions to linearizations to methods of approximation. The fact that this variety of aspects, each examined in considerable detail, can be collected together in a single, unified treat­ ment gives this theory an elegance that we feel sets it apart from many others. While our goal has always been to give a complete treatment of the theory as it now stands, the work here is not meant to be definitive. Theories are not entities that appear suddenly one day and thereafter stand as given. Rather, they must mature and grow with time and experience. Our development is more correctly a beginning, tempting others to explore, appraise, and modify its features so as to produce something better