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| Synge J. L. — Tensor Calculus |
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| Предметный указатель |
Absolute, derivative 49 250 283 311
Absolute tensor
Acceleration 149 153 170
Action metric 177
Affine connection 292
Amorphous space 282
angle 34 36
Angular, momentum 156
Angular velocity
Antipodal space 116
Antisymmetry 15
Bernoulli's integral 202
Bianchi identity 87
Bipolar coordinates 79
Body force 200
Cartesian, coordinates 142
Cartesian tensor
cell 253
Centrifugal force 167
Christoffel symbols 41
Coefficients of connection 287
Comoving time-derivative 191
Compatibility equations 236
Completely applicable 179
components 9 144
Compressed notation 20
Configuration 4
Configuration-space 168
conformal 299
Conjugate metric tensor 31
Connection, coefficients 287
Connection, double 291
Connection linear
Connection, semi-symmetric 308
Connection single
Conservation of mass 195
Continuity equation 196
Contraction 17 88 295
Contraction-invariant connection 291
Contravariant, tensor 11
Contravariant vector
coordinates 3
Coordinates bipolar
Coordinates, geodesic 292
Coordinates geodesic
Coplanar vectors 94 317
Coriolis force 167
Covariant, derivative 51 251 287 311
Covariant tensor
Curl 135 246
Curvature 81 294
Curvature constant
Curvature, Gaussian 96
Curvature geodesic
Curvature, invariant 89
Curvature of curve
Curvature, tensor 83 85 294
Curve 5
Curved space 82
Curvilinear coordinates 26
D'Alembert's principle 159
density 192 241
Derivative, absolute 49 250 283 311
Derivative covariant
Determinant of metric tensor 30
Dilatation 211
Dimension of space 4
Displacement, infinitesimal 9
Displacement null
Distance 28
Distance geodesic
Divergence 57 134 193
Double connection 291
Dual tensors 246
Dummies 7
Dynamics, general system 168
Dynamics, particle 149
Dynamics rigid
Einstein 142
Einstein tensor
Elasticity 202
Elasticity tensor
Electromagnetic radiation 213
Elliptic space 116
Energy 177
Equilibrium of continuous medium 208
Euler equations, calculus of variations 40
Euler equations rigid
Eulerian method 191
Event 126
Excess of angle sum 96
expansion 194 211
Extension, of cell 253 255
Extension strain
Finzi 237
First curvature 73
First integral 45
Flat space 82 118 295
Flat projectively
force 150 171
Frame of reference 162
Frenet formulae 74
frequency 219
Fundamental, form 27 29
Fundamental tensor
future 126
Gauge, invariance 298
Gauge transformation
Gauss 27 96
Gauss' theorem 193
Gaussian curvature 96
Geodesic 37
Geodesic circle
Geometrical, object 10
Geometrical optics
Green's theorem 193 275
Hamilton's, equation 217
Hamilton's principle
Hertz vector 223
Hertzian oscillator 238
Homeomorphic 179
Homogeneous coordinates 119
Hooke's law 209
Hydrodynamics 190
Hyperspace 4
Hypersurface 5
indefinite 29
Indicator 29
Infinitesimal displacement 9
Inner product 17
Instantaneous axis 159
Integral, multiple 258 316
Invariant 12
Invariant curvature
Irrotational flow 199
Isotropic, medium 210
Isotropic point
Jacobian 6 240
Kinematical metric 169
kinetic energy 151 168
Kronecker delta 8
Kronecker delta generalized
Lagrangian, equations 151 174
Lagrangian, method 191
Lame's constant 212
Laplacian 58
Least action 177
Length 29
Levi-Civita 142
Line dement 27
Linear connection 287
Lines of force 174
Local Cartesians 58
Lorentz transformation 140 231
Lowering suffixes 31
| Magnitude of vector 33
Manifold 4
Maxwell's equations 214 228 230
Metric, action 177
Metric form
Metric, kinematical 169
Metric tensor
Mixed tensor 13
Moebius strip 261
Moment, of force 156
Moment of
Motion, continuous medium 208
Motion, Newtonian law 150
Motion perfect
Multiple integral 257 316
Negative transformation 121 249
Neuber 237
Newton's law of motion 150
Non-Riemannian space 282
Normal coordinates 62
Normal vector 63 265
Null, cone 125
Null displacement
Null, geodesic 46
One-sided region 261
Order of tensor 11
Orientation of cell 260
Oriented, region 261
Oriented tensor
Ortho-invariant connection 290
Orthogonal, coordinates 71 145
Orthogonal, trajectories 63
Orthogonal trajectory
Orthogonality 36
Outer product 17
Papcovich 237
Parallel propagation 49 99 288
Parallelogram 292
Parametric line 70
PAST 126
Path 289
Perfect fluid 199
Period 219
Permutation symbol 131 243 249 250
Perpendicularity 36
Phase wave 218
Physical components 144
Plane waves 222
Point 3
Poisson's ratio 212
Polar space 116
Polarization 221
Positive transformation 121 249
Positive-definite 29
Potential, electromagnetic 223 239
Potential, energy 152
PRESENT 126
Pressure 199
Product, inner 17
Product outer
Projective, connection 309
Projective curvature
Proper transformation 121
Raising suffixes 31
Range convention 7
Reconcilable curves 100
Relative, invariant 198
Relative tensor
Relativity, general theory 231
Relativity, special theory 125 155 231
Ricci 142
Ricci principal directions
Ricci tensor 88 295
Riemann 28
Riemannian, coordinates 59
Riemannian curvature
Rigid body 156
Rigidity 212
Scalar product 134
Schroedinger 279
Schur's theorem 112
Semi-symmetric connection 308
Signature 314
Single connection 291
Skew-symmetry 15
Space 4
Space amorphous
Space, non-Riemannian 282
Space of constant curvature
Space-time 125 229
Special theory of relativity 125
Sphere 123
Spherical, polar coordinates 54
Spherical, space 116
Stokes' theorem 267
Stokes' theorem generalized
Straight line 123
strain 202 205
Stream line 235
Stress 202 208
Subinvariant 67
subspace 5 253
Subtensor 67
SubVector 67
Summation convention 7
surface 5
Sylvester's theorem 314
Symmetric connection 292
Symmetry 15
Tangent vector 10
Tensor, absolute 198 241
Tensor Cartesian
Tensor, covariant 13
Tensor curvature
Tensor, dual 246
Tensor Einstein
Tensor, fundamental or metric 26 28 31
Tensor, mixed 13
Tensor order
Tensor, oriented 130 249
Tensor relative
Tests for tensors 18
Thomas 309
topology 116 124 179
Torsion 73
Transformation of Christoffel symbols 48
Transformation of coordinates
Transformation, gauge 298
Transformation Lorentz
Transformation, positive or proper 121 249
Transformation projective
Transitivity 14 241
Translation 157
Two dimensions 89
Two-sided region 261
Unit first normal 73
Unit normal 266
Unit tangent vector 34 72
Unoriented region 261
Variety 4
Vector 9
Vector contravariant
Velocity 147 153 169
Velocity
Volume 262
Vortex line 235
Vorticity 196 197
Wave equation 215
Wave-length 219
Weight 240
Weyl space 297
Young's modulus 212
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