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，在系统分析方法论的基础上，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 Equations of motion of locally changeable continuous medium
2.4.3 Equation of balance of inertial mass for locally changeable continuous medium
2.4.4 Equations 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-deformatorgroup
3.4 Transvective-dllation decomposition of k-deformators
3.4.1 Transvectlons, dilations, dilators and homothettes
3.4.2 Transvection-dflatlon decompositions of k-deformator group by Cavaliert group
3.4.3 Transvection-dflatlon decompositions 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
3.5.2 Kinematics equations on the groups □（数理化公式） and □（数理化公式）
3.5.3 Left-hand polar decomposition of k-deformator group
3.5.4 Non-circular (potential) deformation of medium
3.6 Additive decompositions of medium point velocities
3.6.1 Transvective-dilation decomposition
3.6.2 Polar decompositions
3.6.3 Geometrical incompressibility of medium
4 Elements of dynamics of locally changeable continuous medium
4.1 Dynamic and static equations of continuous media
4.2 Quasi-linear continuous media
4.3 Conditions for continuous medium entirety
4.4 Elements of dynamics of ideal fluid
4.4.1 Dynamic equations of ideal fluid
4.4.2 Equations of thermodynamics for ideal fluid
4.5 Elements of H-class dynamics
4.5.1 Dynamic equations 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
4.6.4 P23-class of quasi-linear continuous media
4.7 Elements of dynamics for quasi-linear continuous NPL-media
4.7,1 Equations 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 equations
4.8.2 Dynamic equations
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 motions
5.2.2 Kinematics of simple free and related motions
5.2.3 Kinematics of simple free motion in presence of constructive shifts and rotations
5.2.4 Kinematics of simple constrained motion
5.2.5 Kinematics of composite motion
5.3 Fundamentals for representations of group of rigid body rotations.
5.3.1 Exact representation of group of two-dimensional rotations in Rodrigues-Hamilton rotation group
5.3.2 Covering of group of 3-dimensional rotations 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 Equations of rigid body motion
5.4.1 Equations of simple free motion
5.4.2 Equations of simple constrained motion of rigid body
5.4.3 Motion equations of body bearing dynamically unbalanced and asymmetric rotation bodies
5.4.4 Free rigid body motion in inertial external medium
5.4.5 Simple motion equ