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| Lee A. — Mathematics Applied to Continuum Mechanics |
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| Предметный указатель |
Adherence boundary condition 86
Adjoint 560—561
Adverse pressure gradient 120
Airy function 377
Airy stress function 242—245
Alternating tensor 35 222
Alternator 16
Amplitude dispersion 435
Antisymmetric tensor 41
Antisymmetric tensor, vector of 46—47
Banach space 563
Barotropic fluid 68
Beam, vibrating 518—521 530—531
Beetles, wave pattern from 379—380
Bell, E.T. 475
Beltrami equation 68
Beltrami — Michell equations 171—172
Bending 194—215
Bending, moment 202
Bending, pure 199
Bessel functions 365—367
Bessel inequality 558
Betti — Rayleigh reciprocal theorem 183
Biharmonic equation 242 245
Biorthogonality 562
Birkhoff, G. 125
Blasius similarity solution 116—119
Bluff body 121
Bluman, G.W. 125
Body force 159
Bond number 325
Born, M. 533
Boundary conditions, boundary layer 111—113
Boundary conditions, elastic 208—210 216
Boundary conditions, natural see "Natural boundary conditions"
Boundary conditions, viscous 85—86
Boundary conditions, water wave 301—314
Boundary layer 77 105—114
Boundary layer equations 111
Boundary layer equations, difference scheme for 139—143
Boundary layer equations, Mises transformation for 114—115
Boundary layer, chemical reaction in 127—128
Boundary layer, separation of 120 122—124
Boundary operator 515
Bounded set 564
Brachistochrone 461—462 469 470 473 475 485
Brillouin, L. 380
Brown, S. 124
Bryson, A. 328
Buckling 212—214 486
Built-in end 208
Bulk, modulus 166
Bulk, phase 308
Cable, hanging 487 493
Calculus of variations 461
Capillary waves 340 380 435
Carrier, G.F. 77
Cartesian tensor 33 also
Catenary 493
Cauchy sequence 563
Cauchy — Green deformation tensor 186—187
Center of mass 195
Centroid 195
Characteristic equation 52 514
Characteristic line 404
Characteristic polynomial 52
Characteristic value 52
Characteristic vector 52
Chemical reaction, in boundary layer 127—128
Chester, C. 378
Cofactor 18
Cole, J.D. 125
Compact set 564
Compatibility conditions 153—155 167—168
Complementary error function 101
complete 556
Complete set 515
Complete space 563
Completely continuous operator 564
Complex sums 349—352
Compression 165—166
Concentrated load 217—218
Condon, E.U. 516
Conformal mapping 122
Consistency, condition 434
Consistency, requirement 23—27
Constant coefficients, linear partial differential equations with 336
Constitutive equation for heat flow 89
Constitutive equation for linear elasticity 160—162
Constitutive equation for nonlinear elasticity 188—189
Constitutive equation for surface tension 307
Constitutive equation for viscous fluids 80—85
Constraint 450—457 479—485
Continuum mechanics, basic equations of 72
Contour integration 364
Contraction product 39
Contraction product, matrix of 42
Contraction, of a tensor 37
Convergent, sequence 563
coordinates 3—4
Couette flow 93—95 96
Couette flow, stability of 102—103
Couple stress tensor 70
Courant max-min principle 528—532
Courant, R. 143
Covariance 25
Cramer's rule 19
Critical angle 277
Curl 62
Curvature 314 487
Curvature, mean 317
D'Alembert's paradox 105
Davey, A. 443
Deformation tensor 79 186
Del operator 62
Delay lines 284
Delta function 360—363
Dense set 509
Determinants 16—22
Diagonalizatton, of a tensor 59
Diaz — Weinstein formula 239
Differentials 29 78
Diffusion 102 126—127
Dilatation 152 155
Dilatation, speed 270
Dilatation, waves 260
Direction vector 10
Dirichlet integral 489
Dirtiness, quasi-equilibrium 440
Discontinuity surfaces, propagation of 264—271
dispersion 211—212 243—294 340 381
Dispersion, anomalous 212 340
Dispersion, nonlinear 435
Dispersion, normal 340
Displacement 144
Displacement thickness 114
Dissipation, viscous 89—90
Divergence 62
Divergence, Theorem 64 66
Domain perturbations 423
Doppler shift 403
Drag coefficient 118
Drag on a sphere 137
Dual spaces 561
Dubois — Remond lemma 497
Dyad 38 49
Dyadic 49
Dym, C.L. 212
Dynamic boundary condition 304—314 316
Ed rule 20
| Eiconal equations 270
Eigenvalues 49—59 552
Eigenvalues as minima 505—507
Eigenvalues as stationary values 504—505
Eigenvalues, nonlinear 427
Eigenvalues, perturbed 566
Eigenvalues, simple 566
Eigenvectors 52—53
Elastic constants, relations between 167
Electrostatic potential 546
End, built in 208
End, free 209
End, simply supported 208
Energy balance 70—71 174—176
Energy of wave system 365
Energy, conservation 354
Energy, kinetic 89 176 487
Energy, potential 89 179—181 214 494—495 534—536
Energy, propagation 397—398
English, W.J. 526
Equilibrium and potential energy 214
Equilibrium, equations in elasticity 171
Equilibrium, local 309
Equipollent stress 235
Equivoluminal waves 260
Erdelyi, A. 415
Erickson, J.L. 460
Error function 101
Ether, elastic 168 277
Euclidean space 4
Euler equation 463—467 471—473 475 499
Euler — Bernoulli rule 200
Euler — Lagrange equation see "Euler equation"
Exact solutions to elasticity equations 162—166
Exact solutions to viscous flow equations 93—102
Experiment, comparison with, in water waves 382—388
Extension, simple 155 192
Extremalizalion of a function 448—457
Extremalizalion of potential energy in elasticity 494—495
Extremum 448
Faddeyeva, V. 519
Fermat's principle 491
Ffowes-Williams, J.F. 345
Fife, P. 437
Filaments 199
Finite deformation 184—191
First variation 497
Fishing line, flow past 341
Flexural rigidity 200
Flexure 200
Fluegge, S. 460
Fourier coefficients 556
Fourier integrals 355—359
Fourier series 352—353
Free end 209
Frequency, local 393
Friedberg, R. 465
Friedman, B. 378
Friedrichs, K. 143
Froude number 325
Functional 462 504
Fundamental 435
Gadd, G. 388
Gauss's theorem 65 66
Gee, D. 386
Geodesics 487
Gerstner's trochoidal wave 315
Gradient 62
Gram determinant 524
Gravity waves 340 435
Green's function 218
Greenspan, H. 104
Group lines 397
Group speed 368 374—380
Group velocity 391—400
Gurtin, M.E. 235
Gyration, radius of 206
Hahn, W. 536
Hamilton's equations 401
Hamilton's principle 486 495
Hanratty, T. 439
Harmonic generation 435
Hawkings, D. 345
Heat, diffusion 126—127
Heat, flux vector 71 89
Helium ionization potential, and Ritz method 516
Helmholtz representation theorem 67
Hilbert space 563
Homogeneous deformation 189
Homogeneous material 161
Hooke's law, generalized 162
Hoop stress 250
Hunter, C. 408
Identity tensor 44
Impermeable boundary 301
Incompatibility tensor 158
Index, dummy 6
Index, free 6
Inequality constraints 455—457
Inertia, moments of 195
Inertia, principal axes of 195
Inertia, products of 195
Inertia, rotary 207
Inertia, tensor 195
Infinitesimal strain 147 150
Influence function 218
inhomogeneous equation 560
Inhomogeneous media, waves in 401
Inner product 549
Integrability 153
Intermediate variable 113
Intrinsic reference quantities 330
Invariance 25
Invariance and energy balance 70—71
Inverse method 233
Irrotational flow 79
Irrotational waves 260
Isoperimetric inequality 491
Isoterm 450
Isotropic 82
Isotropic material 161
Isotropic tensor 43—46
Jacobian 148—149
Jacobian, derivative of 21—22
Jeffreys, H. 284
Joseph, D. 423
Jump conditions 218 266—271
Kajiura, K. 389
Keller, H.B. 264
Keller, J.B. 386
Kelvin effect 191
Keyes, T. 85
Kim, Y. 439
Kinematic boundary condition 301—302
Kinematic viscosity 87
kinetic energy 89 176 487
Kino, G.S. 284
Kirsch problem 248—250 257—258
Kranzer, H.C. 386
Kreyszig, E. 366
Kronecker delta 7
Kuba, E. 386
Lagerstrom, P.A. 124
Lagrange multiplier 452—457 480—482 501—502
Lagrange — Cauchy theorem 69
Lagrangian 486
Lagrangian, description 144
Lame constants 162
Landau, L. 499
Laplace transform 363
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