本书共分八章，主要阐述了变分原理，即自然界静止（相对稳定状态）事物中的一个普遍适应的数学定律，也称最小作用定理，是物理学中的一条基本原理。书中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。本书由浅入深，逻辑严谨，适合高等院校师生及相关专业研究者和爱好者参考阅读。

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 8
Bibliography
编辑手记