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| Ïîèñê ïî óêàçàòåëÿì |
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| Nayfeh A.H. — Perturbation Methods |
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| Ïðåäìåòíûé óêàçàòåëü |
Limit, Oseen's 140
Limit, Stokes' 140 see also Inner limit; Intermediate limit; and Outer limit
Limitations of, method, of composite expansions 153—154
Limitations of, method, of matched asymptotic expansions 144—145 155 156 303 339
Limitations of, method, of multiple scales 269—270 275—276 302—303
Limitations of, method, of strained coordinates 79 98—103 107 109 110 302 303
Limitations of, Struble's method 174
Limitations of, von Zeipel's procedure 199
Lindstedt — Poincare technique 56 57 58—60 95 96 185 200
Linear damped oscillator, treated by multiple scales 228—243
Linearization, method of 57 94—95
Liouville — Green approximations 49 320 335
Liouville — Green approximations, higher 315—317
Liouville — Green approximations, successive 324—325
Liouville — Green transformation 308 315 340
Liouville, equation 236 380 382
Liouville, problem 314
Logarithms 7 12 45 83 137 144 308 311
Lommel functions 353
Long period part 169 191 209 214
Lunar motion 60; see also Earth-moon-spaceship problem
Mach number 26 83 85
Matched asymptotic expansions, method of 37 48 51 78 110—144 148 153 154 235 317 346 378 384
Matched asymptotic expansions, method of, applied to turning point problems 336—339
Matched asymptotic expansions, method of, limitations of 144 155 156 303
Matching 51 110 114 115 116
Matching as guide to forms of expansions 141
Matching of inner and outer expansions, bending of plates 130—132
Matching of inner and outer expansions, caustic problem 378
Matching of inner and outer expansions, earth-moon-spaceship problem 139
Matching of inner and outer expansions, equation with variable coefficients 124
Matching of inner and outer expansions, flow past a sphere 141—144
Matching of inner and outer expansions, simple example 120—121
Matching of inner and outer expansions, slider bearing 127
Matching of inner and outer expansions, term by term 130
Matching of inner and outer expansions, thermoelastic waves 135—136
Matching of inner and outer expansions, turning point problems 337—339 343—344
Matching, asymptotic, principle see van Dyke's principle
Matching, intermediate 119
Matching, Kaplun's, principle 119
Matching, Prandtl, procedure 112 118
Matching, refined 118—119
Mathien equation 339
Mathien equation, exercises involving 53 104 223 303 304
Mathien equation, treated, by averaging using canonical variables 183—185
Mathien equation, treated, by Lindstedt — Poincare technique 60—62
Mathien equation, treated, by method of multiple scales 253—257
Mathien equation, treated, by von Zeipel's procedure 194—200
Mathien equation, treated, by Whittaker's method 62—64
Maxwell's heat conduction law 45
Membrane 356
Method, of multiple scales see Multiple scales method
Method, of strained coordinates see Strained coordinates method
Method, of strained parameters see Strained parameters method
Missile dynamics 233
Missile dynamics, exercises involving 304 305 306
Missile dynamics, linear 320—321
Missile dynamics, nonlinear 291—295
Model for nonlinear instability 50
Model for nonlinear instability, exercises involving 55
Model for nonlinear instability, illustrating limitations of method of strained coordinates 99—100
Model for nonlinear instability, straightforward expansion for 25—26
Model for nonlinear instability, treated, by method of multiple scales 264—266
Model for nonlinear instability, treated, by method of renormalization 96—97
Momenta 179 182 190 199 224
Moon see Earth-moon-spaceship problem; Lunar motion
Multiple scales, method of 51 97 100 153 221 228—307 315 317 339 368 384
Multiple scales, method of, applied, to caustic 379
Multiple scales, method of, to equations with slowly varying coefficients 318—320
Multiple scales, method of, to Orr — Sommerfeld equation 360
Navier — Stokes equations 28 33 39
Neumann, expansion 361; see also Born expansion
Neumann, series 364
Newtonian theory 79
No-slip condition 33 34
Node 252
Nondispersive waves 78 269—270 303.
Nonuniformity, dependence of, on coordinates 49—51
Nonuniformity, dependence of, on size of domain 24—31 38 42
Nonuniformity, in airfoil theory 28 50
Nonuniformity, in asymptotic expansions 16—18
Nonuniformity, in bending of plates 37
Nonuniformity, in Born's expansion 367
Nonuniformity, in Duffing's equation 24—25 49—50
Nonuniformity, in earth-moon-spaceship problem 45
Nonuniformity, in equation with constant coefficients 32
Nonuniformity, in flow past a sphere 31
Nonuniformity, in geometrical optics approximation 376—377
Nonuniformity, in interior of domain 137
Nonuniformity, in jet instability 99
Nonuniformity, in linear oscillator 229
Nonuniformity, in model for nonlinear instability 26 50
Nonuniformity, in relaxation oscillations 35
Nonuniformity, in shift in singularity 43 79
Nonuniformity, in slider bearing 126
Nonuniformity, in thermoelastic waves 47—48
Nonuniformity, in turning point problems 49 284 315 336
Nonuniformity, variable exhibiting 57 285 and
Normal solution 58 60 66 311 326 331 332
Olver's transformation 341 384 385
Operator 206
Operator, adjoint 164
Operator, Faa de Bruno 192
Operator, intensity 372
Operator, mass 371 381
Operator, self-adjoint 163 164
Optics see Geometrical optics
Optimal, control 79
Optimal, coordinate 50 51
Orbit 64 99
Orbital mechanics 233
Order symbols 8 9
Orr — Sommerfeld equation 233 360
oscillations 25 34 89 226 232 303
Oseen's equation 141
Oseen's expansion 140—144
Oseen's limit process 140 141
Oseen's variable 143
Outer expansion 110 112 114 119 146
Outer expansion for bending of plates 128—129
Outer expansion for earth-moon spaceship problem 45 138
Outer expansion for equation with variable coefficients 124
Outer expansion for simple example 117
Outer expansion for slider bearing 126
Outer expansion for thermoelastic waves 47—48
Outer expansion, definition of 117
Outer limit 112 117 119 128 138 144
Outer region 113 122
Outer solution 111 113 115
Outer variable 119 121 144 145
overlapping 113 119
Parabolic coordinates 79
Parabolic cylinder function 344 378
Parabolic equation 37 38 99 379
Paradox 31
PARAMETER 89
Parameter, large 315; see also Turning point problems
Parameter, perturbation 1—4 16 308 method
Parameters 201; see also Variation of parameters
Parametric resonance see Mathieu equation; Stability of elliptic triangular points
Parametrization 88 92
Partitioning see Asymptotic partitioning
Pascal triangle 205
Pendulum 103 224;
Period 169 191 192
Periodic 58 60
Periodic motion 189
Periodic orbit 99
Periodic solutions 34 77
Perturbations, coordinate 4—7 308—314
| Perturbations, parameter 1—4 16 308
Phase 178 380
Phase, rapidly rotating 168 201 234
Phase, speed 76 77
plasma 58 78 216 217 226 234 235 367
Plasticity 90
Plates see Unsymmetrical bending of plates
Poincare — Lighthill — Kuo method see Lighthill's technique
Poisson ratio 36 47
Potential function 26 83 89
Prandtl's boundary layer 113
Prandtl's technique 111 114
Pritulo's technique see Renormalization method
Quantum 58 371;
Random 361 362 363 365 367 369 372 380 381 382
Rankine — Hugonoit relation 84
Ratio Test 6 7 10 11 16
Rayleigh wave speed 47 134
Rayleigh — Schrodinger method 56 71
Rayleigh — Schrodinger method, applied to eigenvalue problem 68—71
Rayleigh — Taylor instability 77 235
Reaction kinetics 79
Reentry dynamics see Missile dynamics
Region of nonuniformity 17 18 19 23 79
Region of nonuniformity for earth-moon-spaceship problem 137—138
Region of nonuniformity for equation with constant coefficients 116
Region of nonuniformity for flow past a sphere 140
Region of nonuniformity for thermoelastic waves 134—135
Region of nonuniformity for turning point problems 284 336
Region of nonuniformity, near a caustic 377—378
Related equation 341
Relaxation oscillations 34—35
Renormalization, method of 57 95—98 308 361 367—372
Renormalization, method of, exercises involving 103 106 107 108
Resonance 89 233 248
Resonance in linear systems 321—324
Resonance, external 225
Resonance, internal 185 225
Resonance, near 195
Resonance, parametric 235
Resonance, passage through 233 see also Harmonic resonance
Resonance, perfect 189
Reynold's equation see Slider bearing
Reynolds number 40 360
Reynolds Number, high 33 130
Reynolds number, small 28 29 139
Rigidity, flexural 36
Ritz — Galerkin procedure 58
Rossby wave 77 234
Rytov's method 361 373
Saddle point 252
Satellite 233 276
Scales 51 110 230 231 232 233 242 303; method
Scattering 57 95 235 361 364 367 368
Schroedinger equation 56 71 160 339 342 344 346
Secular terms 23—26
Secular terms, elimination of 65—68 261 288 302
Self-sustained oscillations 89; see also van der Pol oscillator
Series see Asymptotic series; Lie series and transforms
Shadow boundary 378
Sharp change 103 110 303
Shell 233
Shift 42 77 79 106
Shift in singularity 103
Shift, exercises involving 52 53 106 107
Shift, straightforward expansion for 42—43
Shift, treated, by Lighthill's technique 79—82
Shift, treated, by renormalization 98
Shift, treated, by Temple's technique 94—95
Shock waves 52 78 83 84 85 99 100 235
Short period part 169 191 214
singular 17 57 78 81 231
Singular perturbation 17 99 340
Singular perturbation, dependence on region size 38 42
Singular point, definition of 309 310
Singular point, expansion near an irregular 309—312 326—327
Singular point, regular 5 308
Singularity 85 86
Singularity as a jump discontinuity 32 35
Singularity, branch point 82
Singularity, essential 7
Singularity, growing 23 42 43 45 95
Singularity, logarithmic 45 83 102 137
Singularity, turning point with 358—359
Singularity, worst 81 98
Skin layer 111
Slider bearing 54 125—128
Small parameter multiplying highest derivative 23 31—37 99 317—318
Small parameter multiplying highest derivative in limitations of method of strained coordinates 99 100—102
Smoothing, method of 308 361 380—382
Solvability condition 152 288 302;
Sonic boom 78
Sources of nonuniformity 23—55 140
Spaceship see Earth-moon-spaceship problem
Speed 56 57 58 76 77 83 90 91
Sphere see Flow past a sphere
spherical 28 78 224
Spring 232. See also Duffing equation; Swinging spring
Stability 60 77 78 99 100 162—164 235 252 353 360.
Stability of elliptic triangular points, treated, by method of multiple scales 259—262 275
Stability of elliptic triangular points, treated, by method of strained parameters 64—66
Stability of elliptic triangular points, treated, by Whittaker's technique 66—68
Statistical mechanics 236
Stochastic 361 367
Stokes' expansion 140
Stokes' limit process 140
Stokes' solution 30
Stokes' variable 143
Strained coordinates, method of 51 52 56—109 110 114 156 235 302 303
Strained parameters, method of 56 58—77 78 79 97 99 100 103 105 106
Straining, dependent variable 99 108
Straining, function 57 78 79 81 87 99 101 102 103 107
Straining, of characteristics 87 89
Stratification 216
Stream function 28 29 33 40 57 113 140
Stretching transformation, for bending of plates 128
Stretching transformation, for caustic 377—378
Stretching transformation, for dependent and independent variables 134
Stretching transformation, for earth-moon-spaceship problem 137—138
Stretching transformation, for equation with variable coefficients 122 123
Stretching transformation, for heat equation 151
Stretching transformation, for turning point problems 284 336
Struble's method 171—174 176 183 194 223
Stuart — Watson — Eckhaus technique 162—164
Subnormal solution 311 331—332
Supersonic airfoil theory 50 78 93
Supersonic airfoil theory, straightforward expansion for 26—28
Supersonic airfoil theory, treated, by Lighthffl's technique 86—89
Supersonic airfoil theory, treated, by renormalization 97—98
Swinging spring, exercises involving 105 225
Swinging spring, treated, by averaging Hamiltonian 185—189
Swinging spring, treated, by Lie series and transforms 214—216
Swinging spring, treated, by method of multiple scales 262—264
Temple's technique 57 94—95
Thermoelastic waves, straightforward expansion for 45—48
Thermoelastic waves, treated by method of matched asymptotic expansions 133—137
Thomas — Fermi model 235
Three body problem 199 233 276.
Transfer of boundary condition 27
transform see Lie series and transforms
Transformation, canonical 181 190 191 199
Transformation, contracting 140
Transformation, Deprit 202
Transformation, Hori 202
Transformation, Lie 201
Transformation, Liouville — Green 49 315 340
Transformation, near identity 51 57 168 190 201
Transformation, stretching 111 113 114 116 117 377
Transformation, vonZeipel 171 191 199 202
Transition 380; see Turning point problems
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