经典力学与微分几何(英文)

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