●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
編輯手記

本書共分八章，主要闡述了變分原理，即自然界靜止（相對穩定狀態）事物中的一個普遍適應的數學定律，也稱最小作用定理，是物理學中的一條基本原理。書中內容包括變分法的表達方式、變分法的一些技巧、勒讓德變換。在經典力部分，論述了拉格朗日形式導出哈密頓形式、哈密爾頓運動方程、正則變換方程、運動方程、曲面定義、測地線的法向性質、第二基本形式和點為臍點的緊湊表面。本書由淺入深，邏輯嚴謹，適合高等院校師生及相關專業研究者和愛好者參考閱讀。