伽利略理论力学——连续力学基础 (***)弗拉基米尔·科诺普列夫 著 (***)阿尔·切列门斯基 译 mobi 下载 网盘 caj lrf pdf txt 阿里云

伽利略是第一个把实验引进力学的科学家，他利用实验和数学相结合的方法确定了一些重要的力学定律。本书强调和发展了伽利略力学的基本原理，在系统分析方***的基础上，全面阐述了多体系统力学的数学形式和工作工具。本质上以一种新的方式来描述一类具有环境体的一般多体系统的约束微分方程的设计问题。本书共七章，内容包括引言、力学的几个宇宙及其基本性质、局部线性变介质的运动学、局部线性变连续介质动力学要素、刚体力学、树形结构多体系统力学及代数螺旋理论的建立等。本书适合高等院校数学和力学领域的研究者和研究人员及兴趣爱好者参考阅读。

Preface

1 Introduction

2 The geometrical universe of mechanics and its primary properties

2.1 Axioms of kinematics

2.2 Axioms of dynamics

2.3 Generalized Galtlean group on mechanics universe

2.4 Secondary properties of geometric universeof mechanics

2.4.1 Dynamics homogeneity and lsotropy of geometric universe of mechanics

2.4.2 Equati*** of motion of locally changeable continuous medium

2.4.3 Equation of balance of inertial mass for locally changeable continuous medium

2.4.4 Equati*** of energy balance for locally changeable continuous medium

3 Kinematics of locally linearly changeable medium

3.1 Kinematics equation on k-deformator group

3.2 Deformation matrix and its relation with medium displacement and with k-deformator

3.3 Generatricesofk-deformat***roup

3.4 Transvective-dllation decomposition of k-deformators

3.4.1 Transvectl***,dilati***,dilators and homothettes

3.4.2 Transvection-dflatlon decompositi*** of k-deformator group by Cavaliert group

3.4.3 Transvection-dflatlon decompositi*** of k-deformator group by Cavalterl generalized group

3.5 Polar decomposition of k-deformator group

3.5.1 Right-hand polar decomposition of k-deformator group

……

3.5.3 Left-hand polar decomposition of k-deformator group

3.5.4 Non-circular (potential) deformation of medium

3.6 Additive decompositi*** of medium point velocities

3.6.1 Transvective-dilation decomposition

3.6.2 Polar decompositi***

3.6.3 Geometrical incompressibility of medium

4 Elements of dynamics of locally changeable continuous medium

4.1 Dynamic and static equati*** of continuous media

4.2 Quasi-linear continuous media

4.3 Conditi*** for continuous medium entirety

4.4 Elements of dynamics of ideal fluid

4.4.1 Dynamic equati*** of ideal fluid

4.4.2 Equati*** of thermodynamics for ideal fluid

4.5 Elements of H-class dynamics

4.5.1 Dynamic equati*** of H-class of media

4.5.2 Thermodynamic equation

4.6 Elements of P-class dynamics

4.6.1 Group of rheologtcal coefficient matrices-P-media of II type

4.6.2 P12-class of quasi-linear continuous media

4.6.3 P13-class of quasi-linear continuous media

4.*** P23-class of quasi-linear continuous media

4.7 Elements of dynamics for quasi-linear continuous NPL-media

4.7,1 Equati*** of mechanical state and dynamics for NPL-medta

4.7.2 Thermodynamics equation

4.8 Elements of dynamics of R-class

4.8.1 Mechanical state equati***

4.8.2 Dynamic equati***

4.8.3 Thermodynamics equation

5 Rigid body mechanics

5.1 A rigid body

5.2 Rigid body kinematics

5.2.1 Simple and composite moti***

5.2.2 Kinematics of *** free and related moti***

5.2.3 Kinematics of *** free motion in presence of c***tructive shifts and rotati***

5.2.4 Kinematics of *** c***trained motion

5.2.5 Kinematics of composite motion

5.3 Fundamentals for representati*** of group of rigid body rotati***.

5.3.1 Exact representation of group of two-dimensional rotati*** in Rodrigues-Hamilton rotation group

5.3.2 Covering of group of 3-dimensional rotati*** by Rodrigues-Hamliton group

5.3.3 Kinematics equation on Rodrigues-Hamilton sphere

5.3.4 Cayley-Klein group and its representation in Rodrigues-Hamilton group

5.3.5 Representation of rotation group in Cayley-Klein rotation group

5.3.6 Representation of rotation group in multtpltcative group of quart-body

5.4 Equati*** of rigid body motion

5.4.1 Equati*** of *** free motion

5.4.2 Equati*** of *** c***trained motion of rigid body

5.4.3 Motion equati*** of body bearing dynamically unbalanced and asymmetric rotation bodies

5.4.4 Free rigid body motion in inertial external medium

……

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