Page 369 - Intro to Tensor Calculus

INDEX 363

A
Cauchy stress law 216
Absolute differentiation 120
Cauchy-Riemann equations 293,321
Absolute scalar field 43
Charge density 323
Absolute tensor 45,46,47,48
Christoffel symbols 108,110,111
Acceleration 121, 190, 192
Circulation 293
Action integral 198
Codazzi equations 139
Addition of systems 6, 51
Coefficient of viscosity 285
Addition of tensors 6, 51
Cofactors 25, 26, 32
Adherence boundary condition 294
Compatibility equations 259, 260, 262
Aelotropic material 245
Completely skew symmetric system 31
Affine transformation 86, 107
Compound pendulum 195,209
Airy stress function 264
Compressible material 231
Almansi strain tensor 229
Conic sections 151
Alternating tensor 6,7
Conical coordinates 74
Ampere’s law 176,301,337,341
Conjugate dyad 49
Angle between vectors 80, 82
Conjugate metric tensor 36, 77
Angular momentum 218, 287
Conservation of angular momentum 218, 295
Angular velocity 86,87,201,203
Conservation of energy 295
Arc length 60, 67, 133
Conservation of linear momentum 217, 295
Associated tensors 79
Conservation of mass 233, 295
Auxiliary Magnetic field 338
Conservative system 191, 298
Axis of symmetry 247
Conservative electric field 323

B Constitutive equations 242, 251,281, 287
Continuity equation 106,234, 287, 335
Basic equations elasticity 236, 253, 270
Contraction 6, 52
Basic equations for a continuum 236
Contravariant components 36, 44
Basic equations of fluids 281, 287
Contravariant tensor 45
Basis vectors 1,2,37,48
Coordinate curves 37, 67
Beltrami 262
Coordinate surfaces 37, 67
Bernoulli’s Theorem 292
Coordinate transformations 37
Biharmonic equation 186, 265
Coulomb law 322
Bilinear form 97
Covariant components 36, 47
Binormal vector 130
Covariant differentiation 113,114,117
Biot-Savart law 336
Covariant tensor 46
Bipolar coordinates 73
Cross product 11
Boltzmann equation 302,306
Curl 21, 173
Boundary conditions 257, 294
Curvature 130, 131, 134, 149
Bulk modulus 251
Curvature tensor 134, 145
Bulk coefficient of viscosity 285
Curvilinear coordinates 66, 81
Cylindrical coordinates 18, 42, 69
C
Cartesian coordinates 19,20,42, 67, 83
Cartesian tensors 84, 87, 226