连续介质力学中的数学模型-第2版 本书特色

本书是一部教科书，书中主要介绍连续介质中的数学模型，包括连续介质的一些基本概念、术语和定理，以及流体力学、固体力学中常用的一些模型；同时还介绍了力学中的一些波现象。 要目：（一）连续力学中的基本概念：系统运动描述；动力学基本原理；柯西应力张量的应用；形变张量、形变率张量和本构定律；能量方程和激波方程（二）流体物理学：牛顿流体的一般特性；非粘性流；粘性流和热力学；磁流体动力学和等离子体的惯性约束；燃烧方程；大气及海洋运动方程。（三）固体力学：线性弹性的一般方程；经典问题；能量定理；非线性本构定律和均匀化问题。（四）波现象介绍：力学中的线性波动方程，kdv方程，非线性薛定谔方程。 读者对象：应用数学、物理学、力学和相关专业的大学高年级本科生和低年级研究生。

连续介质力学中的数学模型-第2版 内容简介

　　《连续介质力学中的数学模型（第2版）》是作者精心为广大读者朋友们编写而成的，可以让更多的读者朋友们从书中了解到更多的知识，从而提升读者朋友们自身的知识水平。让我们跟随作者的脚步来更好的阅读《连续介质力学中的数学模型（第2版）》中的内容。《连续介质力学中的数学模型（第2版）》可作为物理、力学专业高年级本科生及应用数学、物理学和工程类的研究生的教材和参考书。

连续介质力学中的数学模型-第2版 目录

Preface
A few words about notations
PART I FUNDAMENTAL CONCEPTS IN CONTINUUM MECHANICS
1 Describing the motion of a system： geometry and kinematics
1.1 Deformations
1.2 Motion and its observation （kinematics）
1.3 Description of the motion of a system： Eulerian and Lagrangian derivatives
1.4 Velocity field of a rigid body： helicoidal vector fields
1.5 Differentiation of a volume integral depending on a parameter
2 The fundamental law of dynamics
2.1 The concept of mass
2.2 Forces
2.3 The fundamental law of dynamics and its first consequences
2.4 Application to systems of material points and to rigid bodies
2.5 Galilean frames： the fundamental law of dynamics expressed in a non—Galilean frame
3 The Canchy stress tensor and the Piola—Kirchhoff tensor.Applications
3.1 Hypotheses on the cohesion forces
3.2 The Canchy stress tensor
3.3 General equations of motion
3.4 Symmetry of the stress tensor
3.5 The Piola—Kirchhoff tensor
4 Real and virtual powers
4.1 Study of a system of material points
4.2 General material systems： rigidifying velocities
4.3 Virtual power of the cohesion forces： the general case
4.4 Real power： the kinetic energy theorem
5 Deformation tensor， deformation rate tensor，constitutive laws
5.1 Further properties of deformations
5.2 The deformation rate tensor
5.3 Introduction to rheology： the constitutive laws
5.4 Appendix.Change of variable in a surface integral
6 Energy equations and shock equations
6.1 Heat and energy
6.2 Shocks and the Rankine——Hugoniot relations

PART Ⅱ PHYSICS OF FLUIDS
7 General properties of Newtonian fluids
7.1 General equations of fluid mechanics
7.2 Statics of fluids
7.3 Remark on the energy of a fluid
8 Flows of inviscid fluids
8.1 General theorems
8.2 Plane h'rotational flows
8.3 Transsonic flows
8.4 Linear accoustics
9 Viscous fluids and thermohydraulics
9.1 Equations of viscous incompressible fluids
9.2 Simple flows of viscous incompressible fluids
9.3 Thermohydranlics
9.4 Equations in nondimensional form： similarities
9.5 Notions of stability and turbulence
9.6 Notion of boundary layer
10 Magnetohydrodynamics and inertial confinement of plasmas
10.1 The Maxwell equations and electromagnetism
10.2 Magnetohydrodynamics
10.3 The Tokamak machine
11 Combustion
11.1 Equations for mixtures of fluids
11.2 Equations of chemical kinetics
11.3 The equations of combustion
11.4 Stefan—Maxwell equations
11.5 A simplified problem： the two—species model
12 Equations of the atmosphere and of the ocean
12.1 Preliminaries
12.2 Primitive equations of the atmosphere
12.3 Primitive equations of the ocean
12.4 Chemistry of the atmosphere and the ocean Appendix.The differential operators in spherical coordinates

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自然科学 数学 应用数学

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