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| Авторизация |
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| Aris R. — Vectors, Tensors and the Basic Equations of Fluid Mechanics |
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| Предметный указатель |
Acceleration 39
Acceleration, physical components 177
Base vector 142
Base vector, variation of 168
Basis: of non-coplanar vectors 13
Basis: reciprocal 20 152
Beltrami's differential parameters 222
Bernoulli equation, engineering 132
Bernoulli theorems 131
Binary mixture 248
Binary mixture, transport in 252
Bird, R.B. 7 132 253
Bjorgum, O. 65 73 74 75
Cartesian coordinates 9 132—133
Cauchy — Stokes decomposition theorem 94
Cauchy's equation of motion 102 178—179 190
Cauchy's reciprocal theorem 104
Cauchy's reciprocal theorem, stress principle 99
chemical potential 251
Chemical reaction 245
Chemical reaction, equilibrium relations 249
Chemical reaction, heat of 251
Chemical reaction, rate of 248
Christoffel symbols: definition of 162
Christoffel symbols: in cylindrical polar coordinates 165
Christoffel symbols: in orthogonal coordinates 164
Christoffel symbols: in spherical polar coordinates 165
Christoffel symbols: in surface coordinates 199—201
Cofactor: alien 266
Cofactor: definition of 266
Coleman, B.D. 133
Conservation of energy 250
Conservation of matter 245
Conservation of momentum 249
Constitutive equations 107 124 188
Constitutive equations, for a surface 232
Constitutive equations, general theory of 190
Constitutive equations, specializations of 124
Continuity equation 87 123
Continuity equation, in cylindrical polar coordinates 178
Continuity equation, in spherical polar coordinates 178
Continuum, idea of 2
Contraction 23
Coordinate lines 194
Coordinate systems 134
Coordinates: cartesian 134
Coordinates: converted 77 183
Coordinates: cylindrical polar 135 143 165 178 182
Coordinates: geodesic 204
Coordinates: Lagrangian 77
Coordinates: material 77 176
Coordinates: orthogonal 143
Coordinates: spatial 77
Coordinates: spherical polar 135 165 178 183
Coordinates: surface 193
Coordinates: surface, transformations of 194
Coordinates: transformation of 9 135
Coordinates: transformation of, proper 136
Covariant differentiation 166
Curtiss, C.F. 7
Curvature: Gaussian 235
Curvature: Gaussian, of a surface 210 221
Curvature: principal, of a surface 221
Curvature: total, of a surface 210 221
Dahler, J.S. 112
Deformation 88
Deformation, principal axes of 92 106
Derivative: converted 78 185
Derivative: covariant 167
Derivative: intrinsic 166 176
Derivative: material 78
Derivative: of hybrid tensors 215
Derivative: surface 209
Determinant: definition of 265
Determinant: derivative of 267
Determinant: expansion of 266
Determinant: Laplacian 268
Determinant: product 268
Diffusion: forced 252
Diffusion: of heat 251
Diffusion: of matter 251
Diffusion: pressure 252
Diffusion: thermal 252
Dilatation 83 180 188
Dilatation, material derivative of 83—84
Dissipation function 118
Divergence, in orthogonal coordinates 170
Dyad 34
Dyadic 34
Dyadic, scalar of 35
Dyadic, vector of 35
Eisenhart, L.P. 74
Eliassen, J.D. 237
Energy: conservation of 124
Energy: dissipation of, by viscous forces 117—118 121—122
Energy: equation of 120
Energy: internal 121
Energy: kinetic 117 121
Energy: strain 118 121
Enthalpy 122 250
entropy 122
Entropy, rate of change of 122
Equation of continuity 87 123 178 236 246
Equation of state 121 124
Equation of state, specializations of 124
Ericksen, J.L. 160
Euclidean space 172
Euler, L. 97
expansion 83
Ferrar, W.L. 74
Feshbach, H. 7 36
Fick's law 121
Flow: axisymmetric 127
Flow: barotropic 130—132
Flow: boundary layer 128—129
Flow: compressible 126
Flow: creeping 127
Flow: irrotational 132
Flow: isentropic 126 130
Flow: plane 125
Flow: steady 79 127
Fluid: incompressible 88 105 125 129
Fluid: isotropic 106
Fluid: Maxwellian 115 192
Fluid: Newtonian 110—111 113 121 125 130 180 189 242
Fluid: non-newtonian 109
Fluid: nonelsatic 107
Fluid: perfect 105 129 180
Fluid: piezotropic 130
Fluid: Stokesian 106—110 119 121
Fluid: surface 234
Forces: body 99
Forces: body, rate of doing work 117
Forces: contact 99
Forces: external 99
Forces: internal 99
Fredrickson, A. G. 253
Frohlich, H. 189
Function: explicit 276
Function: implicit 276
Fundamental forms, relation between 218
Gauss — Codazzi equations 218
Gauss, C.F. 58
Geodesic 201—204
Geodesic, curvature 209
Gerstner wave 79 84
Godal, T. 73 75
Grad, H. 112
Gradient of a scalar 51
Green's theorem 58 171
| Green's theorem, in a surface 223
Grew, K.E. 253
Group: affine 139
Group: linear homogeneous transformation 139
Group: orthogonal 139
Group: properties of 137—138
Group: rotation 139
Group: subgroup of 138
Heat of reaction 251
Hirschfelder, J. O. 7
Hydrostatics 127
Ibbs, T. L. 253
Ideal gas 130
Indices, conservation of 136 141
Integral: line 42
Integral: multiple, change of variable 50
Integral: surface 44
Integral: volume 48
Interface: cylindrical 243
Interface: plane 242
Interface: spherical 243
Interface: surface equations as boundary conditions for 241
Interfacial tension 231
Internal energy 250
Isotropy 105
Jacobian 50 137 276
Jacobian, intrinsic derivative of 177
Jeffreys, B.S. 36
Jeffreys, H. 36
Kellogg, O.D. 59 62 74
Kelvin's theorem 132
Kelvin, Lord 61
Kinematic viscosity 114
Kinematics 76 123
Klein, F. 138
Kronecker delta 10 144 197
Lagrange, J.L. 58
Landan, L.D. 112
Laplacian 54 169 222
Laplacian in orthogonal coordinates 170
Lifshitz, E.M. 112
Lightfoot, E.N. 253
Linear equations 267
Linear equations, homogeneous 267
Lomont, J.S. 73
Mass: conservation of 87 123
Mass: flux 247
Mass: flux, barycentric 247
Material indifference, principle of 192
Matrix algebra, laws of 263
Matrix: addition 264
Matrix: adjugate of 267
Matrix: antisymmetric 261
Matrix: definition of 260 264
Matrix: derivative of 267
Matrix: inverse of 265
Matrix: multiplication 264
Matrix: partitioned 268
Matrix: scalar multiplication of 264
Matrix: singular 266
Matrix: symmetric 261
Matrix: symmetric, canonical form of 271
Matrix: symmetric, latent root of 270
Matrix: symmetric, vector of 270
Matrix: transpose of 264
Mayer, A. 262
Merk, H.J. 245 253
Metric, time dependent 228
Molar flux 247
Momentum: angular 102
Momentum: angular, internal 104 123
Momentum: angular, total 103 123
Momentum: conservation of 99
Momentum: linear 249
Momentum: linear, conservation of 100 123
Momentum: moment of 103
Momentum: moment of, conservation of 123
Momentum: moment of, external 104 123
Morse, P.M. 7 36
Moses, H.E. 73
Motion: Beltrami 125
Motion: Cauchy's equation of 102 113
Motion: complex lamellar 125
Motion: equations of 123
Motion: equations of Newtonian fluid 113
Motion: equations of, specializations of the 124
Motion: irrotational 125
Motion: isochoric 86 124
Motion: restrictions on the type of 124
Navier — Stokes equations 113—116 125 180—183 235 250
Navier — Stokes equations, boundary conditions 115
Navier — Stokes equations, existence of solutions of 115
Navier — Stokes equations, in cylindrical polar coordinates 182
Navier — Stokes equations, in spherical polar coordinates 183
Newell, H.E. 74
Noll, W. 133 191
Oldroyd, J.G. 185 188 189 190
Orthogonality 256
Orthogonality of vectors 15
Parallel vectors, in a surface 206
Particle path 76 77 80 82
Patterson, G.N. 6
Permutation symbol 16 145
Permutation: conjugate 265
Permutation: parity of 265
Phillips, H.B. 36
Point transformation 76
Poisson's equation 70
Power law 109
Pressure: hydrostatic 105
Pressure: thermodynamic 105 108 109
Principal stresses 106
Quadric 259
Quotient rule 29 148
Reynolds number 115
Reynolds' transport theorem 84 178 230
Ricci's lemma 168
Riemann — Christoffel tensor 173 210
Riemannian space 196
Rigid body rotation 89 107
Rigid body rotation, velocity due to 17 25
Rotation of axes 262
Russell, B. 1
Sack, R. 189
Scalar multiplication 11 23 147
Scalar, definition of 3
Scale factor 143
Schild, A. 175
Scriven, L.E. 112 226 244
Second law of thermodynamics 122
Sedov, L.I. 190
Serret — Frenet formulae 42 220
Serrin, J. 37 46 77 98 106 112 120 132 133
Space curve: arc length 40
Space curve: binormal 41
Space curve: closed 39
Space curve: curvature 41
Space curve: osculating plane 40
Space curve: principal normal 41
Space curve: simple 39
Space curve: tangent 40
Space curve: torsion 41
Space: Euclidean 142
Space: Riemannian 172
Specific heat 251
Stewart, W.E. 253
Stoichiometric relations 248
Stokes' hypothesis 180
Stokes' relation 112 114
Stokes' theorem 61 171
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