作者：（罗）拉杜.米龙
页数：256
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560396576
电子书格式：pdf/epub/txt
内容简介
本书是一部英文版的学术专著。本书的目的是提供一个关于阶k≥1的朗格朗日和哈密顿空间的几何理论的简短介绍,同时定义并研究一些新的解析力学几何理论.在本书中,我们将证明可以基于拉格朗日和哈密顿几何来提出这样的理论.相反的,这些几何的构造依赖于机械原理和拉格朗日变换。
目录
1 The Geometry of tangent manifold
1.1 The manifold TM
1.2 Semisprays on the manifold TM
1.3 Nonlinear connections
1.4 N-linear connections
1.5 Parallelism. Structure equations
2 Lagrange spaces
2.1 The notion of Lagrange space
2.2 Variational problem. Euler-Lagrange equations
2.3 Canonical semispray. Nonlinear connection
2.4 Hamilton-Jacobi equations
2.5 Metrical N-linear connections
2.6 The electromagnetic and gravitational fields
2.7 The almost Kahlerian model of a Lagrange space Ln
2.8 Generalized Lagrange spaces
3 Finsler Spaces
3.1 Finsler metrics
3.2 Geodesics
3.3 Cartan nonlinear connection
3.4 Cartan metrical connection
4 The Geometry of Cotangent Manifold
4.1 Cotangent bundle
4.2 Variational problem. Hamilton-Jacobi equations
4.3 Nonlinear connections
4.4 N-linear connections
4.5 Parallelism, paths and structure equations
5 Hamilton spaces
5.1 Notion of Hamilton space
5.2 Nonlinear connection of a Hamilton space
5.3 The canonical metrical connection of Hamilton space Hn
5.4 Generalized Hamilton Spaces GHn
5.5 The almost Kahlerian model of a Hamilton space
6 Cartan spaces
6.1 Notion of Caftan space
6.2 Canonical nonlinear connection of Ln
6.3 Canonical metrical connection of Ln
6.4 The duality between Lagrange and Hamilton spaces
7 The Geometry of the manifold TkM
7.1 The bundle of acceleration of order k≥1
7.2 The Liouville vector fields
7.3 Variational Problem
7.4 Semisprays. Nonlinear connections
7.5 The dual coefficients of a nonlinear connection
7.6 Prolongation to the manifold TkM of the Riemannian structures given on the base manifold M
7.7 N-linear connections on TkM
8 Lagrange Spaces of Higher-order
8.1 The spaces L(k)n = (M,L)
8.2 Examples of spaces L(k)n
8.3 Canonical metrical N-connection
8.4 The Riemannian (k – 1)n-contact model of the space L(k)n
1.1 The manifold TM
1.2 Semisprays on the manifold TM
1.3 Nonlinear connections
1.4 N-linear connections
1.5 Parallelism. Structure equations
2 Lagrange spaces
2.1 The notion of Lagrange space
2.2 Variational problem. Euler-Lagrange equations
2.3 Canonical semispray. Nonlinear connection
2.4 Hamilton-Jacobi equations
2.5 Metrical N-linear connections
2.6 The electromagnetic and gravitational fields
2.7 The almost Kahlerian model of a Lagrange space Ln
2.8 Generalized Lagrange spaces
3 Finsler Spaces
3.1 Finsler metrics
3.2 Geodesics
3.3 Cartan nonlinear connection
3.4 Cartan metrical connection
4 The Geometry of Cotangent Manifold
4.1 Cotangent bundle
4.2 Variational problem. Hamilton-Jacobi equations
4.3 Nonlinear connections
4.4 N-linear connections
4.5 Parallelism, paths and structure equations
5 Hamilton spaces
5.1 Notion of Hamilton space
5.2 Nonlinear connection of a Hamilton space
5.3 The canonical metrical connection of Hamilton space Hn
5.4 Generalized Hamilton Spaces GHn
5.5 The almost Kahlerian model of a Hamilton space
6 Cartan spaces
6.1 Notion of Caftan space
6.2 Canonical nonlinear connection of Ln
6.3 Canonical metrical connection of Ln
6.4 The duality between Lagrange and Hamilton spaces
7 The Geometry of the manifold TkM
7.1 The bundle of acceleration of order k≥1
7.2 The Liouville vector fields
7.3 Variational Problem
7.4 Semisprays. Nonlinear connections
7.5 The dual coefficients of a nonlinear connection
7.6 Prolongation to the manifold TkM of the Riemannian structures given on the base manifold M
7.7 N-linear connections on TkM
8 Lagrange Spaces of Higher-order
8.1 The spaces L(k)n = (M,L)
8.2 Examples of spaces L(k)n
8.3 Canonical metrical N-connection
8.4 The Riemannian (k – 1)n-contact model of the space L(k)n
