Integrable Systems of Classical Mechanics and Lie Algebras
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"Integrable Systems of Classical Mechanics and Lie Algebras" by A. M. Perelomov, Askolʹd Mikhaĭlovich Perelomov is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers.
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"Integrable Systems of Classical Mechanics and Lie Algebras" by A. M. Perelomov, Askolʹd Mikhaĭlovich Perelomov is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Dynamics
Author: A. M. Perelomov, Askolʹd Mikhaĭlovich Perelomov
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers.
| Author | A. M. Perelomov, Askolʹd Mikhaĭlovich Perelomov |
| Publisher | Springer |
| Published | 1990 |
| ISBN-13 | 9783764323363 |
| Binding | Paperback |
| Pages | 328 |
| Language | English |
| Subjects | Electronic books |
| Topic | Dynamics |
Format: Paperback
Length: 328 pages
Language: English
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