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| Ïîèñê ïî óêàçàòåëÿì |
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| Lee A. — Mathematics Applied to Continuum Mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Legendre's necessary condition 475
Level surface 450
Lewy, H. 143
Lifshitz, E. 499
Lighthill, M.J. 105
Lin, C.C. 119
Line element 146
Linear dependence 12
Linear elasticity 169—170 187—188
Linear independence 12 550
Linear operator 551
Linear transformations 28—32
Linearization 326
Local Reynolds number 118
Local velocity field 78—80
Long waves 343—345
Longitudinal waves 260
Longuet-Higgins, M.S. 300
Love waves 289—295
Love, A.E.H. 289
Luke, J.C. 489
Mach angle 411
Mach cone 411
Matching 112—113
Material coordinates 144
Material indifference 85
Matrices, and tensors 41—43
Matrix, definite 449
Maximum 448
Maximum-minimum principle 528—532
Maxwell's equations 168 277
McGoldrick, L.F. 437 439
Mean height requirement 321
Membrane 489 512 537—538
Membrane, analogy 226 545
Metric 563
Meyer, R.E. 86
Michell, J.H. 244
Miles, J.W. 387
Minimization, of potential energy 179—181
Minimum 448
Minor 18
Mises transformation 114—115
moment 195
Moment of area, polar 228
Moment, Diaz — Weinstein formula for 239
Momentum thickness 114
Morton, K. 142
Natural boundary conditions 467—471 493 521—523
Natural laws 533
Navier equations 171
Navier — Stokes equations 84 90—91 93—102 138—139
Neutral axis 199
Newton's second law 23—25
Noda, E. 386
Non-Euclidean space 4
Nonlinear eigenvalue problem 427
Nonlinear traveling waves 418—443
Norm 509
Norm, natural 563
Normal principal 487
Normal stress 50
Normalization condition 430
Normed vector space 563
Observer invariance 85
Oleinik, O.A. 143
Oppenheim, I. 85
Orthogonal eigenvectors 56—57
Orthogonal functions 557
Orthogonal vectors 549
Overlap region 112
P-waves 260
Parallelogram law 13
Particle paths, in gravity waves 342
Patching 111—112
Peclet number 128
Pekeris, C.L. 525
Permutation 15
Permutation, symbol 16
Perturbation theory for eigenvalues 566
Perturbation theory for fluid-air interface 317—319
Perturbation theory for nonlinear water waves 418—443
Phase function 393 408—410
Phase speed 375—380
phase velocity 396—397
Philips, O.M. 300
Physical law, general statement vs. particular version 24—25
Pierson, W.J. 437
Pipe, viscous flow in 104—105
Plane, strain 157 241—250
Plane, stress 250—252 255
Plane, stress, generalized 252—256
Plastic material 160
Plate, boundary layer flow past 107—111 115—119
Plate, elastic 525 545
Pnueli, A. 525
Poiseuille flow 95—98
Poisson's ratio 164
Polar decomposition theorem 184—186
Polar fluids 70
Polarization, plane of 272
Positive operator 539—541 554
potential energy 89 179—181 214
Potential energy, extremalization of 494—495
Potential energy, minimum of 534—536
Prandtl, L. 226
Pressure 322
Principal axes 57 151—152 195
Principal diagonal 52
Principal minor 52
Principle see "Fermat's principle"
Prins, J.E. 382
Projection 4—5
Proportional limit 160
Pythagoras, law of 4
Quasi-elastic material 168
Quotient rule 40
Radiation condition 337 398 410
Range convention 6
Rate-of-strain tensor 79
Rayleigh — Ritz method see "Ritz method"
Rayleigh, impulsive flow 98—102
Rayleigh, Lord 278
Rayleigh, waves 278
Reaction, chemical, in boundary layer 127—128
Real operator 553
Reciprocal theorem, Betti — Rayleigh 183
Rectangular bar, shear of 164—165
Reflection, coefficients 276
Reflection, internal 285—289
Reid, W.H. 562
Resonance, nonlinear 436—440
Resonant energy interchange 442
Resultant 202
Reynolds number 107
Richimyer, R. 142
Rigid body rotation 47 79 195
Ritz method 504 513—521 531—532 542—544
Rotation, finite 13
Rotation, improper 11
Rotation, proper 11
Rotation, rigid body 47 79 195
Rotation, small 13
Rotation, tensor 79 150—151 185
Rotation, vector 151
s-waves 260
Sanchez, D. 536
scalar 34
Scalar, multiple 9
Scalar, product 549
| Scaling 107 329—334
Scattering 272
Schwarz inequality 550
Sears, W. 124
Second order tensors 41
Segel, L.A. 368
Self-adjoint operator 507 546—562 566—567
Self-adjointness, formal 561
Semi-inverse method 219—220
Separation of flow 120
Separation of variables 231—233 343
Sequences 563
Shaw, J. 284
Shear force 202
shear modulus 165
Shear of rectangular bar 164—165
Shear speed 270
Shear strain 151—152
Shear stress 50
Shear stress, maximum of 229 238 460 544
Shear waves 260
Shear, simple 156 189—191
Shorltey, G.H. 516
Sideband perturbations 443
Signum function 351
Similarity solutions 116—119 125—127
Simply supported end 208
Skew-symmetric tensor 41
Slow viscous flow 135—138
Smirnow, V.I. 452
Snell's law 492—493
Solenoidal vector field 67
Solid body rotation 47 79 195
Solitary wave 382
Sphere, slow flow past 135—138
Sphere, Stokes drag formula for 137
St. Venant Principle 235—237
Stability, asymptotic 534
Stability, Liapunov 534
STALL 122
Stationary integral 472
Stationary phase, method of 370 412—416
Stationary point 449
Stationary value problems 500—503
Stewarlson, K. 124 443
Stokes's theorem 65 66
strain 144—150
Strain, energy 175
Strain, infinitesimal 147
Strain, normal 151
Strain, plane 157 241—250
Strain, principal 151
Strain, shearing 151
Strain, tensor 146 149—150
Strain-stress equations 162
Streamlined body 121
Stress 50
Stress, concentration 250
Stress, energy 176
Stress, function 224—225 242—245
Stress, function, modified 229
Stress, plane 250—252
Stress, tensor 25—26 29—32
Stress-strain relations 160—162
Stretch tensor 185
String 489
Struik, D. 317
Stuart, J.T. 442
Sturm — Liouville problem 557
Subharmonic function 229
Suction 104
Summation convention 7
Superposition 346
Surface, free 324
Surface, phase 308
Surface, tension 303
Surface, viscosity 308
Symmetric tensor 41 55—59
Tautochrone 475
Tension, of a cylindrical bar 163—164
Tensor 34 also "Rotation
Tensor and matrix 41—43
Tensor, antisymmetric 41
Tensor, calculus 60—67
Tensor, components 31—32
Tensor, contraction 37 39
Tensor, derivatives 61
Tensor, diagonalization 59
Tensor, difference 35
Tensor, equality 36
Tensor, field 60
Tensor, inertia 195
Tensor, nonsingular 43
Tensor, product 38
Tensor, quotient rule 40
Tensor, real 55
Tensor, scalar multiple 36
Tensor, second order 41—43
Tensor, stress 25—26
Tensor, sum 35
Tensor, symmetric 41 55
Tensor, transformation law 25 34 61
Tensor, transpose 41
Tidal oscillations 525—528
Tidal waves 389
Tides, equations for 345—346
Timoshenko, S. 211
Tornberg, G. 386
Torsion 219—235 541—545
Torsional rigidity 228
Trace 52
Traction 195
Transformation coordinate 5—6
Transformation matrix 10 22
Transformation symbol 7
Transpose, tensor 41
Transposition 15
Transversality condition 485
Transverse waves 260
Trial elements 513
Triangle inequality 414 550
Triple deck 122
Triple scalar product 21
Tsunami 389
Twist modulus 168
Ultimate load 161
Uniqueness theorems, in elasticity 178—179
Unit coordinate vectors 4
Unit tensor 34
Unit vector 10
Ursell, F. 378 402
Van Dorn, W. 388 389 390
Van Dyke, M. 123 124
Variational methods, in elasticity 214—215
Variational notation 497—499
Variational problems 447
Variations, first 497
Variations, weak and strong 472
Vector 9—13 488
Vector identities 23
Vector product 465
Vector space 547—548
Velocity, gradient tensor 79
Velocity, potential 512—513 558
Velocity, profile 94
Velocity, scale 214
Virtual displacements 177 181
Virtual strains 177
Virtual work 177—179
viscosity 84 87
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