Classical Many-Body Problems Amenable to Exact Treatments [electronic resource] : (Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space / by Francesco Calogero.

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.

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.