Classical Many-Body Problems Amenable to Exact Treatments

(Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space

Francesco Calogero (Autor)

Buch | Hardcover

XIX, 550 Seiten

2001
Springer Berlin (Verlag)
978-3-540-41764-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	21.1.2011
Reihe/Serie	Lecture Notes in Physics Monographs
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1200 g
Einbandart	gebunden
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
Schlagworte	Dynamical system • Hamiltonian Many-Body Problem • Lax Pair • Liouville Solvability
ISBN-10	3-540-41764-8 / 3540417648
ISBN-13	978-3-540-41764-4 / 9783540417644
Zustand	Neuware