ENGLISH

The Geometry of Hamilton and Lagrange Spaces

By Dragos Hrimiuc , Hideo Shimada , R. Miron , Sorin V. Sabau

Book information

Publisher
Springer Netherlands
Year
2001
ISBN
0792369262, 9780792369264
LCC
QA689 .G48 2001
Open Library ID
OL18334945M
Language
english
Format
PDF
Filesize
21 MB (22392676 bytes)
Series
Fundamental Theories of Physics
Edition
1
Pages
355\355
Time added
2011-01-06 10:13:16

Description

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.

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