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Lee A. Ч Mathematics Applied to Continuum Mechanics
Lee A. Ч Mathematics Applied to Continuum Mechanics

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Ќазвание: Mathematics Applied to Continuum Mechanics

јвтор: Lee A.

јннотаци€:

This is my favorite text for continuum mechanics.
It contains derivations not usually covered, and spends a lot of time educating the reader on the tensor notation.
As a plus, it contains a supplement on functional analysis applications, which I still consult above some other texts on the subject.
I have almost no complaints about this text. I cannot suggest it enough.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2007

 оличество страниц: 613

ƒобавлена в каталог: 29.01.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
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      169Ч170 187Ч188
Linear independence      12 550
Linear operator      551
Linear transformations      28Ч32
Linearization      326
Local Reynolds number      118
Local velocity field      78Ч80
Long waves      343Ч345
Longitudinal waves      260
Longuet-Higgins, M.S.      300
Love waves      289Ч295
Love, A.E.H.      289
Luke, J.C.      489
Mach angle      411
Mach cone      411
Matching      112Ч113
Material coordinates      144
Material indifference      85
Matrices, and tensors      41Ч43
Matrix, definite      449
Maximum      448
Maximum-minimum principle      528Ч532
Maxwell's equations      168 277
McGoldrick, L.F.      437 439
Mean height requirement      321
Membrane      489 512 537Ч538
Membrane, analogy      226 545
Metric      563
Meyer, R.E.      86
Michell, J.H.      244
Miles, J.W.      387
Minimization, of potential energy      179Ч181
Minimum      448
Minor      18
Mises transformation      114Ч115
moment      195
Moment of area, polar      228
Moment, Diaz Ч Weinstein formula for      239
Momentum thickness      114
Morton, K.      142
Natural boundary conditions      467Ч471 493 521Ч523
Natural laws      533
Navier equations      171
Navier Ч Stokes equations      84 90Ч91 93Ч102 138Ч139
Neutral axis      199
Newton's second law      23Ч25
Noda, E.      386
Non-Euclidean space      4
Nonlinear eigenvalue problem      427
Nonlinear traveling waves      418Ч443
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      56Ч57
Orthogonal functions      557
Orthogonal vectors      549
Overlap region      112
P-waves      260
Parallelogram law      13
Particle paths, in gravity waves      342
Patching      111Ч112
Peclet number      128
Pekeris, C.L.      525
Permutation      15
Permutation, symbol      16
Perturbation theory for eigenvalues      566
Perturbation theory for fluid-air interface      317Ч319
Perturbation theory for nonlinear water waves      418Ч443
Phase function      393 408Ч410
Phase speed      375Ч380
phase velocity      396Ч397
Philips, O.M.      300
Physical law, general statement vs. particular version      24Ч25
Pierson, W.J.      437
Pipe, viscous flow in      104Ч105
Plane, strain      157 241Ч250
Plane, stress      250Ч252 255
Plane, stress, generalized      252Ч256
Plastic material      160
Plate, boundary layer flow past      107Ч111 115Ч119
Plate, elastic      525 545
Pnueli, A.      525
Poiseuille flow      95Ч98
Poisson's ratio      164
Polar decomposition theorem      184Ч186
Polar fluids      70
Polarization, plane of      272
Positive operator      539Ч541 554
potential energy      89 179Ч181 214
Potential energy, extremalization of      494Ч495
Potential energy, minimum of      534Ч536
Prandtl, L.      226
Pressure      322
Principal axes      57 151Ч152 195
Principal diagonal      52
Principal minor      52
Principle      see "Fermat's principle"
Prins, J.E.      382
Projection      4Ч5
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 Ч Ritz method      see "Ritz method"
Rayleigh, impulsive flow      98Ч102
Rayleigh, Lord      278
Rayleigh, waves      278
Reaction, chemical, in boundary layer      127Ч128
Real operator      553
Reciprocal theorem, Betti Ч Rayleigh      183
Rectangular bar, shear of      164Ч165
Reflection, coefficients      276
Reflection, internal      285Ч289
Reid, W.H.      562
Resonance, nonlinear      436Ч440
Resonant energy interchange      442
Resultant      202
Reynolds number      107
Richimyer, R.      142
Rigid body rotation      47 79 195
Ritz method      504 513Ч521 531Ч532 542Ч544
Rotation, finite      13
Rotation, improper      11
Rotation, proper      11
Rotation, rigid body      47 79 195
Rotation, small      13
Rotation, tensor      79 150Ч151 185
Rotation, vector      151
s-waves      260
Sanchez, D.      536
scalar      34
Scalar, multiple      9
Scalar, product      549
Scaling      107 329Ч334
Scattering      272
Schwarz inequality      550
Sears, W.      124
Second order tensors      41
Segel, L.A.      368
Self-adjoint operator      507 546Ч562 566Ч567
Self-adjointness, formal      561
Semi-inverse method      219Ч220
Separation of flow      120
Separation of variables      231Ч233 343
Sequences      563
Shaw, J.      284
Shear force      202
shear modulus      165
Shear of rectangular bar      164Ч165
Shear speed      270
Shear strain      151Ч152
Shear stress      50
Shear stress, maximum of      229 238 460 544
Shear waves      260
Shear, simple      156 189Ч191
Shorltey, G.H.      516
Sideband perturbations      443
Signum function      351
Similarity solutions      116Ч119 125Ч127
Simply supported end      208
Skew-symmetric tensor      41
Slow viscous flow      135Ч138
Smirnow, V.I.      452
Snell's law      492Ч493
Solenoidal vector field      67
Solid body rotation      47 79 195
Solitary wave      382
Sphere, slow flow past      135Ч138
Sphere, Stokes drag formula for      137
St. Venant Principle      235Ч237
Stability, asymptotic      534
Stability, Liapunov      534
STALL      122
Stationary integral      472
Stationary phase, method of      370 412Ч416
Stationary point      449
Stationary value problems      500Ч503
Stewarlson, K.      124 443
Stokes's theorem      65 66
strain      144Ч150
Strain, energy      175
Strain, infinitesimal      147
Strain, normal      151
Strain, plane      157 241Ч250
Strain, principal      151
Strain, shearing      151
Strain, tensor      146 149Ч150
Strain-stress equations      162
Streamlined body      121
Stress      50
Stress, concentration      250
Stress, energy      176
Stress, function      224Ч225 242Ч245
Stress, function, modified      229
Stress, plane      250Ч252
Stress, tensor      25Ч26 29Ч32
Stress-strain relations      160Ч162
Stretch tensor      185
String      489
Struik, D.      317
Stuart, J.T.      442
Sturm Ч 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 55Ч59
Tautochrone      475
Tension, of a cylindrical bar      163Ч164
Tensor      34 also "Rotation
Tensor and matrix      41Ч43
Tensor, antisymmetric      41
Tensor, calculus      60Ч67
Tensor, components      31Ч32
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      41Ч43
Tensor, stress      25Ч26
Tensor, sum      35
Tensor, symmetric      41 55
Tensor, transformation law      25 34 61
Tensor, transpose      41
Tidal oscillations      525Ч528
Tidal waves      389
Tides, equations for      345Ч346
Timoshenko, S.      211
Tornberg, G.      386
Torsion      219Ч235 541Ч545
Torsional rigidity      228
Trace      52
Traction      195
Transformation coordinate      5Ч6
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      178Ч179
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      214Ч215
Variational notation      497Ч499
Variational problems      447
Variations, first      497
Variations, weak and strong      472
Vector      9Ч13 488
Vector identities      23
Vector product      465
Vector space      547Ч548
Velocity, gradient tensor      79
Velocity, potential      512Ч513 558
Velocity, profile      94
Velocity, scale      214
Virtual displacements      177 181
Virtual strains      177
Virtual work      177Ч179
viscosity      84 87
1 2 3
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