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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 ¡õ£¨ÊýÀí»¯¹«Ê½£© and ¡õ£¨ÊýÀí»¯¹«Ê½£© 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