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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. 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.
List of contents
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 Space 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.- Appendices: A: Elliptic Functions.- B: Functional Equations.- C: Hermite Polynomials.- D: Remarkable Matrices and Related Identities.- E: Langrangian Approximation for Eigenvalue Problems in One and More Dimensions.- F: Some Theorems of Elementary Geometry in Multidimensions.- G: Asymptotic Behavior of the Zeros of a Polynomial Whose Coefficients Diverge Exponentially.- H: Some Formulas for Pauli Matrices and Three-Vectors.- References.
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"The book is built in a multilayer (or telescoped , in the authors words) structure, with a very rich index: by looking through the table of contents the reader will easily locate the sections in which a given topic or example is dealt with. Inside each section, a similar structure is present, with a very rich supply of more detailed discussions, remarks, problems and exercises; all of this material is set in different types, so that one can easily navigate through the main line of the book and enter the detail only if and where desired. This will help the reader facing such a complete treatment, both in case of students trying to master the subject through a structured study, and in that of practitioners interested in some specific systems. The book is, in the reviewer s opinion, well suited to both of these uses." (Zentralblatt MATH, 1011, 2003) "A great attention to all details of calculations [...] allows an undergraduate student or just a novice to follow them. Thus, the book combines the features of a scientific monograph and a textbook (or even the syllabus of a special university course). [...] All in all, the book describes part of the modern theory of integrable systems of classical mechanics as seen by one of its creators. It is highly accessible and will serve as a standard reference for a long time." (Mathematical Reviews 2003a)
