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.

The Geometry of Hamilton and Lagrange Spaces PDF

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