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Integrability and nonintegrability in geometry and mechanics

Integrability and nonintegrability in geometry and mechanics Acta Applicandae Mathematicae 28 (1992). 93 Book Reviews A. T. Fomenko: Integrability and Nonintegrability in Geometry and Mechanics, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 1988, 360 pp., ISBN: 90-277-2818-6, Dfl. 252, -/US$149. This excellent book deals with a new direction in modern mathematics: new methods of integration of Hamiltonian systems on symplectic manifolds. The origins of this theory are in classical theoretical mechanics, mathematical physics, Hamiltonian systems, and symplectic geometry. The material presented is based on the author's lectures at the Department of Mechanics and Mathematics at Moscow State University and it includes many recent results obtained and discussed in the seminar 'Modern Geometric Methods' headed by the author at Moscow University in 1984- The book contains six chapters and, taking into account the diversity of the exposed material, we prefer to present each of them separately. Chapter ! is 'Some equations of classical mechanics and their Hamiltonian properties' and presents the basic notions and results which are used in the following chapters of the book: (1) classical equations of motion of a three-dimensional rigid body: the Euler-Poisson equations, the integrable Euler, Lagrange, and Kovalev- skaya cases, general equations related to the motion of a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Integrability and nonintegrability in geometry and mechanics

Acta Applicandae Mathematicae , Volume 28 (1) – May 1, 2004
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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00047032
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae Mathematicae 28 (1992). 93 Book Reviews A. T. Fomenko: Integrability and Nonintegrability in Geometry and Mechanics, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 1988, 360 pp., ISBN: 90-277-2818-6, Dfl. 252, -/US$149. This excellent book deals with a new direction in modern mathematics: new methods of integration of Hamiltonian systems on symplectic manifolds. The origins of this theory are in classical theoretical mechanics, mathematical physics, Hamiltonian systems, and symplectic geometry. The material presented is based on the author's lectures at the Department of Mechanics and Mathematics at Moscow State University and it includes many recent results obtained and discussed in the seminar 'Modern Geometric Methods' headed by the author at Moscow University in 1984- The book contains six chapters and, taking into account the diversity of the exposed material, we prefer to present each of them separately. Chapter ! is 'Some equations of classical mechanics and their Hamiltonian properties' and presents the basic notions and results which are used in the following chapters of the book: (1) classical equations of motion of a three-dimensional rigid body: the Euler-Poisson equations, the integrable Euler, Lagrange, and Kovalev- skaya cases, general equations related to the motion of a

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: May 1, 2004

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