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Aris R. — Vectors, Tensors and the Basic Equations of Fluid Mechanics
Aris R. — Vectors, Tensors and the Basic Equations of Fluid Mechanics



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Название: Vectors, Tensors and the Basic Equations of Fluid Mechanics

Автор: Aris R.

Аннотация:

Introductory text for engineers, physicists and applied mathematicians applies mathematics of Cartesian and general tensors to physical field theories, demonstrating them chiefly in terms of the theory of fluid mechanics. Many exercises throughout the text. Index. Preface. Appendixes.


Язык: en

Рубрика: Физика/Классическая физика/Механика жидкости и газа/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 314

Добавлена в каталог: 18.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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