This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces.
This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.

Klappentext

This book focuses treatable This class on exactly many' body problems. does not include most We are therefore reminded "of physical problems. the of the man home late at after an alcoholic who, story returning night the for his under he was a knew, evening, scanning ground key lamppost; be that he had it somewhere but under the to sure, dropped else, only Yet was there to conduct a searcW' . light lamppost enough proper we feel the interest for such models is nowadays sufficiently widespread because of their their mathematical relevance and their multi beauty, farious that need be made for no our apologies applicative potential choice. In whoever undertakes to read this book will know from any case, its title what she is in for! Yet this title a of it some may require explanations: gloss (including its extended inside front follows. version, see cover) and nonrelativistic "Classical" we mean nonquantal (although By consider the which indeed some are Ruijsenaars Schneider models, treated in this relativistic versions as known, nonre book, of, previously lativistic is focussed see our on models; below): presentation mainly of whose time evolution is determined many body point particles systems Newtonian of motion to by equations (acceleration proportional force).

Inhalt

Classical (Nonquantal, Nonrelativistic) Many-Body Problems.- One-Dimensional Systems - Motions on The Line and on The Circle.- N-Body Problems Treatable Via Techniques of Exact Lagrangian Interpolation in Spaces of One or More Dimensions.- Solvable and/or Integrable Many-Body Problems in The Plane, Obtained by Complexification.- Many-Body Systems in Ordinary (Three-Dimensional) Space: Solvable, Integrable, Linearizable Problems.