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Sokolnikoff I.S. — Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua
Sokolnikoff I.S. — Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua

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Название: Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua

Автор: Sokolnikoff I.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 360

Добавлена в каталог: 24.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-systems      138 152
$\epsilon$-systems, derivatives of      140 180
$\epsilon$-systems, tensor character of      138
Absolute derivative      132
Absolute tensor      73
Acceleration, of a fluid      322
Acceleration, of a particle      198 263
Action, principle of least      219
Admissible functional arguments      153
Admissible transformations      53
Affine transformation      10 83
Algebra of tensors      66—68
Angle, between coordinate lines      122
Angle, between directions in space      121
Angle, between directions on a surface      149
Anisotropic media      315 318
Appell, P.      81 238 262 290 327
Arc length, along a curve in space      135
Arc length, along a curve on a surface      147
Arc length, along coordinate lines      122
Arc length, element of      75 100 110 119 147 193
Area, element of      151
Associated tensors      70
Axiom, of dimensionality, JI Axiom, of parallels      109
Axioms for linear vector spaces      11
Beltrami, E.      110
Bergmann, P. G.      270 288 289 327
Bernoulli, D.      219
Bertrand, J. L. F.      142
Bianchi’s identities      95
Binormal      138
Birkhoff, G. D.      276 280
Bolyai, J.      0
Bolza, O.      221
Bouquet, J. C.      98
Brillouin, L.      290 327
Calculus of variations      352—159
Calculus of variations, fundamental lemma in      154
Calculus of variations, fundamental problem of      154
Cantor      1
Carath$\acute{e}$odory, C.      221
Cartan, E.      98
Cauchy — Schwarz inequality      194
Cauchy, A. L.      307 318
Cayley, A.      116
Center of mass      258
Characteristic values of matrices      33 37
Chou, P. Y.      280
Christoffel symbols      78
Christoffel symbols, transformation of      82
Christoffel, E. B.      84
Closure, property of      55
Codazzi equations      186
Collar, A. R.      237
Compatibility, equations of      300
Components of tensors      51 62
Components of tensors, laws of transformation for      61—63
Components of vectors      8 13
Components of vectors, physical      8 126
Conservation, of energy      209 218 273
Conservation, of mass      273 317
Conservative force fields      203 218
Continuity, equation of      322
Contraction, in relativity      264
Contraction, of tensors      67
Contravariant and covariant laws      59 62
Contravariant and covariant laws, tensor character of      64
Contravariant transformation      57
Contravariant vector      59
Coordinate curves (or lines)      118
Coordinate surfaces      118
Coordinate systems      1 10
Coordinate systems, construction of      1
Coordinate systems, oblique cartesian      3
Coordinate systems, orthogonal cartesian      3 13
Coordinates, curvilinear      116 143
Coordinates, curvilinear, cylindrical      119
Coordinates, curvilinear, Gaussian      145
Coordinates, curvilinear, generalized      223
Coordinates, curvilinear, geodesic      163
Coordinates, curvilinear, local      268
Coordinates, curvilinear, normal      48
Coordinates, curvilinear, orthogonal      122 150
Coordinates, curvilinear, proper      268
Coordinates, curvilinear, spherical      53 118
Coordinates, curvilinear, transformation of      10 52
Correspondence, one-to-one      1 9
Cosine of an angle      194
Courant, R.      257
Covariant and contravariant laws      59 62
Covariant and contravariant laws, tensor character of      64
Covariant derivative of a tensor      85—87
Covariant differentiation      84—88
Covariant differentiation, formulas for      87
Covariant differentiation, inversion of order of      91 92
Covariant tensor      61
Covariant transformation      57
Covariant vector      59
Cramer’s Rule      19
Curl of a vector, in cartesian coordinates      249
Curl of a vector, in curvilinear coordinates      251
Curvature vector      139
Curvature, Einstein      169
Curvature, Gaussian      168 187
Curvature, geodesic      171
Curvature, lines of      191
Curvature, mean      187
Curvature, normal, of a surface      189
Curvature, of a curve      137
Curvature, radius of      189
Curvature, total      168 187
Curvatures, principal      191
Curve, motion of particle on a      207
Curves, coordinate      118
Curves, in space      135
Curves, on a surface      187
Curvilinear coordinates, in space      116
Curvilinear coordinates, on a surface      143
D'Alembert's principle      309
Darboux, G.      98
Dedekind, J. W. R.      1
Deflection of light rays      288
Deformation, of space      26
Deformation, of space, analysis of      291—296
Deltas, Kronecker      13 19 100 105
Density, scalar      72
Derivative, absolute      132
Derivative, covariant      85 87
Derivative, intrinsic      132
Derivative, of a base vector      129
Derivative, of a tensor      85 87
Derivative, of a vector      85 128
Derivative, of an invariant      86
Derivative, tensor      178
Descartes, R.      1
Determinants      18 105
Determinants, differentiation of      107
Determinants, expansion of      19 106
Determinants, functional      54
Determinants, multiplication of      18 106
Determinants, Vandermondian      34
Dickson, L. E.      34
Differentiation, covariant      84
Differentiation, intrinsic      131
Differentiation, tensor      178
Dilatation      305
Dimensionality of space, axiom for      11
Direction moment      148
Direction, in space      120 194
Direction, on a surface      148
Displacement vector      4 198 295
Distance, Euclidean      119 193
Distortion of volume elements      303
Divergence of a vector, in cartesian coordinates      247
Divergence of a vector, in curvilinear coordinates      247
Divergence of a vector, in cylindrical coordinates      250
Divergence of a vector, in orthogonal curvilinear coordinates      251
Divergence of a vector, in plane polar coordinates      250
Divergence of a vector, in spherical coordinates      250
Divergence theorem      247
Duncan, W. J.      237
Dynamics, of $n$ particles      223
Dynamics, of a particle      199
Dynamics, of rigid bodies      223
Dynamics, relativistic      275
e-systems      100 107 151
e-systems, application of, to determinants      105
Eddington, A. S.      276 288 289 327
Einstein curvature      169
Einstein's energy equation      271
Einstein, A.      61 95 264 265 267 273 275 289
Einstein’s gravitational equations      275
Einstein’s postulates      265
Einstein’s tensor      95
Eisenhart, L. P.      161 166 186 327
Elastic constants      317
Elasticity, equations of      318
Energy      201
Energy, conservation of      209 218 273
Energy, equation of      273
Energy, integral of      218
Energy, internal      315
Energy, kinetic      203
Energy, potential      203
Energy, strain      315
entropy      315
Equilibrium, differential equations of      307
Ether      204
Euclidean space      4 25 75 00 112
Euclid’s axiom of parallels      109
Euclid’s Elements      109
Euler, L.      157 219
Eulerian hydrodynamical equations      324
Eulerian strain tensor      293
Euler’s equations      155—159
Extremals of functionals      153 157 159
Extremum, constrained      159 233
Fermi, E.      165
Field, conservative      203
Field, tensor      63
Field, vector      128
Fitzgerald, G. F.      207
Fluid, incompressible      323
Fluid, perfect      323
Fluid, viscous      320
Flux of a gravitational field      251
force      199
Forces, external and internal      230
Forces, generalized      228
Forces, reactive      230
Forces, workless      230
Frazer, R. A.      237
Free indices      18
Frenot formulas      139—141
Frequency equation      237
Functional      153
Functions, linear vcctor      25
Functions, of class $C^{n}$      53
Functions, scalar point      56
Fundamental quadratic form, first      145 147
Fundamental quadratic form, second      177 181
Fundamental tensor      76
Galilean transformations      263
Galileo      199
Gauss, C. F.      110 143 177 246
Gauss, equation of      186
Gauss, formulas of      183
Gaussian curvature      168
Gauss’ equations of a surface      143
Gauss’ flux theorem      253
Generalized coordinates      223
Generalized force      228
Generalized momentum      239
Generalized velocities      224
Generalized virtual displacements      231
Geodesic coordinates      163—165
Geodesic curvature      171
Geodesics      159 161
Geodesics, trajectories as      229
Geometrization of dynamics      222 229
Geometry, Lobachevskian      115
Geometry, metric      111
Geometry, non — Euclidean      109
Geometry, of space curves      135
Geometry, Riemannian      112
Gravitation, Einstein’s law of      275
Gravitation, Newton’s law of      242
Gravitational field, constant      206
Green, G.      246
Green’s function      256
Green’s theorems      248 256
Griffith, B, A.      238 262
Group, abstract      55
Groups, isomorphic      57
Hamilton, W. R.      199 219
Hamiltonian function      239
Hamilton’s equations      238
Hamilton’s principle      216
Hermitean matrices      48
Hilbert, D.      257
Holonomic systems      225
Hooke’s law      317
Hydrodynamics, equations of      324
Hydrostatic pressure      320
Ideal fluid      323
Incompressible fluid      323
Indices, free      18
Indices, summation      17
Inertial systems      198
Infinitesimal strains      300 318
Inner product of tensors      69
Integrability conditions      98 183 300
interval      269
Intrinsic differentiation      131
Intrinsic geometry      143 145 167
Invariance, concept of      51
Invariance, of physical laws      263
Invariance, transformation by      55
Invariants      52
Invariants, derivatives of      86
Irrotational motion      325
Isometric surfaces      167
Isotropic media      315
Jacobi, C. G. J.      219 221
Jacobian determinants      54
Kellogg, O. D.      246 247
Kepler’s law      242 261
Killing’s equations      311
kinetic energy      203
Kinetic potential      228
Klein, P.      116
Kronecker deltas      13 19 100
Kronecker deltas, derivatives of      108
Kronecker deltas, tensor character of      105
Lagrange, J. L.      199 219
Lagrangean equations of motion      204 221 225
Lagrangean function      205
Lagrangean strain tensor      293
Lam$\acute{e}$'s constants      317
Landau, L.      289
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