醉染图书伽利略理论力学——连续力学基础9787560397108

Preface

1 Introduction

2 The geometrical universe of mechanics and its primary properties

2.1 Axioms of kinematics

2.2 Axioms of dynamics

. Generalized Galtlean group on mechanics universe

2.4 Secondary properties of geometric universeof mechanics

2.4.1 Dynamics homogeneiyndlstropy 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 decoition of k-deformators

3.4.1 Transvectlons,dilations,dilators and homothettes

3.4.2 Transvection-dflatlon decoitions of k-deformator group by Cavaliert group

3.4.3 Transvection-dflatlon decoitions of k-deformator group by Cavalterl generalized group

3.5 Polar decoition of k-deformator group

3.5.1 Right-hand polar decoition of k-deformator group

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3.5.3 Left-hand polar decoition of k-deformator group

3.5.4 Non-circular (potential) deformation of medium

3.6 Additive decoitions of medium point velocities

3.6.1 Transvective-dilation decoition

3.6.2 Polar decoitions

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 si-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 P-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 coite motions

5.2.2 Kinematics of simple free and related motions

5.. Kinematics of simple free motion in presence of constructive shifsndrtations

5.2.4 Kinematics of simple constrained motion

5.2.5 Kinematics of coite 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

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