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The Geometry of Hamilton and Lagrange Spacesby Radu Miron
Synopses & Reviews
This monograph presents for the first time the foundations of Hamilton Geometry. The concept of Hamilton Space, introduced by the first author and investigated by the authors, opens a new domain in differential geometry with large applications in mechanics, physics, optimal control, etc. The book consists of thirteen chapters. The first three chapters present the topics of the tangent bundle geometry, Finsler and Lagrange spaces. Chapters 4-7 are devoted to the construction of geometry of Hamilton spaces and the duality between these spaces and Lagrange spaces. The dual of a Finsler space is a Cartan space. Even this notion is completely new, its geometry has the same symmetry and beauty as that of Finsler spaces. Chapter 8 deals with symplectic transformations of cotangent bundle. The last five chapters present, for the first time, the geometrical theory and applications of Higher-Order Hamilton spaces. In particular, the case of order two is presented in detail. Audience: mathematicians, geometers, physicists, and mechanicians. This volume can also be recommended as a supplementary graduate text.
Book News Annotation:
For those working in the field of analytical mechanics, the geometric concepts of Lagrange space and Hamilton space are new. Hamilton space as a geometric theory of the Hamiltonian function, introduced by Miron (Al. I. Cuza U., Iasi, Romania) and investigated with his coauthors, opens a new domain in differential geometry with applications to problems of electromagnetism, gauge theory, and relativity in mechanics, optimal control, and physics. Prior to elaborating on the natural connection between Lagrange and Hamilton spaces, the authors overview the geometry of the tangent bundle and Finsler spaces. Then they discuss the cotangent bundle T*M and Hamilton space of higher order. Includes 178 references. This monograph is suitable as a supplementary graduate text.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
Includes bibliographical references (p. 323-335) and index.
Table of Contents
Preface. 1. The geometry of tangent bundle. 2. Finsler spaces. 3. Lagrange spaces. 4. The geometry of cotangent bundle. 5. Hamilton spaces. 6. Cartan spaces. 7. The duality between Lagrange and Hamilton spaces. 8. Symplectic transformations of the differential geometry of T* M. 9. The dual bundle of a k-osculator bundle. 10. Linear connections on the manifold T*2M. 11. Generalized Hamilton spaces of order 2. 12. Hamilton spaces of order 2. 13. Cartan spaces of order 2. Bibliography. Index.
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