作者：(印)娜姆·柯布拉加德(Namdeo K
页数：439页
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560394831
电子书格式：pdf/epub/txt
内容简介
本书共分八章, 主要阐述了变分原理。内容包括变分法的表达方式、变分法的一些技巧、勒让德变换。在经典力部分, 论述了拉格朗日形式导出哈密顿形式、哈密尔顿运动方程、正则变换方程、运动方程、曲面定义、测地线的法向性质、第二基本形式和点为脐点的紧凑表面。
目录
Preface
Chapter 1
Variational Principle and Lagrange’s Equations
Hamilton’s Principle
Some Techniques of Calculus of Variations
Derivation of Lagrange Equations From Hamilton’s Principle
Extension of Principle to Non Holonomic Systems
Conservation Theorems and Symmetry Properties
Chapter 2
Legendre Transformations and the Hamilton Equations of Motion
Cyclic Coordinates and Conservation Theorems
Routh’s Procedure and Oscillations about Steady Motion
The Hamiltonian Formulation of Relativistic Mechanics
The Principle of Least Action
Chapter 3
The Equations of Canonical Transformation
Examples of Canonical Transformation
The Simplistic Approach to Canonical Transformations
Poisson Brackets and Other Canonical Invariants
Chapter 4
Equations of Motion
Infinitesimal Canonical Transformations and Conservation
Theorems in the Poisson Bracket Formulation
The Angular Momentum
Poisson Bracket Relations
Symmetry Groups Of Mechanical Systems
Liouville’s Theorem
Chapter 5
Definition of surface
Curves on a surface
Surfaces of revolution
Helicoids
Metric
Direction coefficients
Families of curves
Isometric correspondence
Intrinsic properties
Geodesics
Canonical geodesic equations
Chapter 6
Normal property of geodesics
Existence theorems
Geodesic parallels
Geodesic curvature
Gauss Bonnet theorem
Gaussian curvature
Surfaces of constant curvature
Conformal mapping
Geodesic mapping
Chapter 7
Chapter 1
Variational Principle and Lagrange’s Equations
Hamilton’s Principle
Some Techniques of Calculus of Variations
Derivation of Lagrange Equations From Hamilton’s Principle
Extension of Principle to Non Holonomic Systems
Conservation Theorems and Symmetry Properties
Chapter 2
Legendre Transformations and the Hamilton Equations of Motion
Cyclic Coordinates and Conservation Theorems
Routh’s Procedure and Oscillations about Steady Motion
The Hamiltonian Formulation of Relativistic Mechanics
The Principle of Least Action
Chapter 3
The Equations of Canonical Transformation
Examples of Canonical Transformation
The Simplistic Approach to Canonical Transformations
Poisson Brackets and Other Canonical Invariants
Chapter 4
Equations of Motion
Infinitesimal Canonical Transformations and Conservation
Theorems in the Poisson Bracket Formulation
The Angular Momentum
Poisson Bracket Relations
Symmetry Groups Of Mechanical Systems
Liouville’s Theorem
Chapter 5
Definition of surface
Curves on a surface
Surfaces of revolution
Helicoids
Metric
Direction coefficients
Families of curves
Isometric correspondence
Intrinsic properties
Geodesics
Canonical geodesic equations
Chapter 6
Normal property of geodesics
Existence theorems
Geodesic parallels
Geodesic curvature
Gauss Bonnet theorem
Gaussian curvature
Surfaces of constant curvature
Conformal mapping
Geodesic mapping
Chapter 7
