|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Nayfeh A.H. — Perturbation Methods |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Acoustic 77 78
Aerodynamic 110
Airfoil theory 98 99 235 303;
Airy's equation 312 336
Airy's functions 49 336 378
Algebraic equation 2 57 74 95 327
Algorithm 168 171 199 209
Algorithm for canonical systems 212—214
Algorithm, generalized 202—206
Algorithm, simplified 206—208
Anomaly 79
Aperiodic motion 189
Astrophysics 235
Asymptotic expansion 23 78
Asymptotic expansion of Airy's functions 337
Asymptotic expansion of Bessel's function 16
Asymptotic expansion, definition of 12
Asymptotic expansion, divergent 16
Asymptotic expansion, elementary operation on 18—19
Asymptotic expansion, uniform 17—19
Asymptotic expansion, uniqueness of 14 see also Asymptotic series
Asymptotic matching principle see Matching
Asymptotic partitioning 327—331
Asymptotic sequence 12 14 16 18 19
Asymptotic sequence, factorial 12
Asymptotic sequence, fractional powers in 136 137
Asymptotic sequence, logarithms in 137 144
Asymptotic series 10—12
Asymptotic series, definition of 11
Asymptotic series, versus convergent series 15—16 see Asymptotic expansion
Attenuation 46 78
Averaging, generalized method of 168—171 191 211 223—225 231
Averaging, Krylov — Bogolinbov — Mitropolski, method of 174—179 183 194 211 212 223 224 246 248
Averaging, method of 159—227
Averaging, Struble's method of 171—174 176 183 194 223
Averaging, using, canonical variables 179—189
Averaging, using, Lagrangian 216—222
Averaging, using, Lie series and transforms 200—216
Averaging, van der Pol's method of 164—165 see also Smoothing
Averaging, von Zeipel transformation 189—200
Beam, vibration of 105 106 155 226 306
Bearing, slider 54 125—128
Bellman, equation of 22
Benard problem 77
Bending of, shells and tubes 54 353;
Benney's technique 38—42
Bernoulli's equation 83
Bessel functions 1 5 6 15 312 315 383
Bessel functions, asymptotic expansion of 16 312—314 329—331
Bessel functions, integral representation of 16 314
Bessel functions, zeros of 21
Bethe — Salpeter equation 372
Blunt body problem 99
Boltzmann's equation 236
Born approximation 362
Born expansion 308 361—367 373
Born expansion, renormalization of 367—372
Boundary conditions, loss of 31 34 37 38 54 111 114 122
Boundary conditions, transfer of 27
Boundary layer 18 23 79 111 112 147 233
Boundary layer, location of 114—116 122
Boundary layer, Prandtl 34
Boundary layer, problem with two, s 128—133
Boundary layer, stability of 353
Branch point 82
Bretherton's equation, exercises involving 227 306
Bretherton's equation, treated, by method of multiple scales 266—269 298—300
Bretherton's equation, treated, by variational approach 217—221
Bretherton's equation, wave-wave interaction for 219—221 266—269
Brownian motion 236
Buckling 233
Canonical equations 180 199
Canonical, averaging, variables 179—189
Canonical, Jordan, form 327
Canonical, mixed, variables 199
Canonical, system 190 201
Canonical, transformation 181 187 191
Canonical, variables 181 183 184 195 202 216 224
Caustic 234 375—380
Change 111 113
Change of characteristics 89 see also Sharp change; Type change of
Characteristic exponent 58 62 66
Characteristic, parameters 89 94
Characteristic, wave speeds 91
Characteristics, expansion in terms of 57 86—94 303
Characteristics, method of 374
Circuit, electronic see van der Pol oscillator
Cluster expansions 363
Compatability relationship 217 222
Composite expansion 114 144 384 385
Composite expansion for earth-moon-spaceship problem 139
Composite expansion for equation with variable coefficients 125
Composite expansion for simple example 121—122
Composite expansion for slider bearing 128
Composite expansion for thermoelastic waves 136
Composite expansion for unsymmetrical bending of plates 133
Composite expansion, construction of 121
Composite expansions, applied to turning point problems 348—350
Composite expansions, method of 144—154 317 318
Composite solution 113
Conservation form of equations 226
Coordinate, optimal 50—51
Coordinate, parabolic 79
Coordinate, perturbations 1 4—7 21 309—314 379
Coordinate, role of, systems 23 49—52 54 380
Correlation 363
Cosmological expansion 233
Cycle, limit 35
Cylinder, a solid, expanding 83—86
Cylinder, elliptic 346
Cylindrical, functions 358 378 380
Cylindrical, jet 99
Degenerate 72 74
Derivative—expansion procedure 302
Derivative—expansion procedure, applications of 243—269
Derivative—expansion procedure, description of 230 236—240
Derivative—expansion procedure, limitations of 269—270 see also Multiple scales method
Detuning 250
Diagram 366 367
Diagram, bare 364
Diagram, connected 370 371 372
Diagram, double 365
Diagram, dressed 365
Diffraction 346 380
Diffusion equation 38
Dirichlet problem 38
Discontinuity see Singularity
Dispersion relationship 178 217 218 219 220 222 227 266 301
Dispersive waves 78 234 303
Dispersive waves, long nonlinear 38—42 see also Bretherton's equation; Klein — Gordon equation; Thermo-elastic waves; Wave-wave interaction
Divisor, small 196
Domain, effect of, on nonuniformity of expansions 38 42
Domain, infinite 24—31
Duffing equation 50 51
Duffing equation with slowly vary coefficients 286
Duffing equation, exercises involving 54 104 105 223 224 304
Duffing equation, straightforward expansion for 24—25
Duffing equation, treated, by averaging using canonical variables 182—183
Duffing equation, treated, by derivative-expansion procedure 243—245
Duffing equation, treated, by generalized method of multiple scales 286—291
Duffing equation, treated, by Krylov — Bogoliubov method 167
Duffing equation, treated, by Krylov — Bogoliubov — Mitropolski method 175—176
Duffing equation, treated, by Lindstedt — Poincare method 58—60
Duffing equation, treated, by renormalization 95—96
Duffing equation, treated, by Struble's method 171—174
Duffing equation, treated, by two-variable expansion procedure 271—273
Duffing equation, treated, by von Zeipel's procedure 192—194
Dyson equation 371 381
Earth-moon-spaceship problem 233 302 303
Earth-moon-spaceship problem, exercises involving 53 107
| Earth-moon-spaceship problem, illustrating limitations of method of strained coordinates 102—103
Earth-moon-spaceship problem, straightforward expansion for 43—45
Earth-moon-spaceship problem, treated, by Lighthill's technique 82—83
Earth-moon-spaceship problem, treated, by method of composite expansions 153—154
Earth-moon-spaceship problem, treated, by method of matched asymptotic expansions 137—139
Earth-moon-spaceship problem, treated, by method of multiple scales 295—298
Eccentricity 64 233 346
Edge layer 111
Eiconal equation 374 377 379
Eigenvalue 56
Eigenvalue problem, linear 68—71
Eigenvalue problem, quasilinear 71—76
Elastic 46 58 90 353
Elastic waves 89—94
Elliptic equation 37 42 98 189 234 303 360
Energy level 56 58
Entropy layer 79
Euler — Lagrange equation 216 217 218 220 222
Faa de Bruno operators 192
Feynman diagrams 308 361—372
Flight mechanics 233
Floquet theory 60 62 64 66
Flow past a sphere, exercise involving 158
Flow past a sphere, straightforward expansion for 28—31
Flow past a sphere, treated by method of matched asymptotic expansions 139—144
Flow through a channel 54 56 216
Flow, down an inclined plane 38—42 99
Flow, hypersonic 79
Flow, jet 99
Flow, past a body 33—34 113
Flutter 234
foci 253
Fokker — Planck equation 235 381
FOURIER 45 167 178
frequency 56 58 96 165 252
Fresnel diffraction 380
Frobenius, method of 5 310
Gauge, function 7 8
Gauge, transformation 232
Gaussian 363 367 369 372
Generalized expansion see Composite expansion
Generalized method of averaging see Averaging method
Generalized vector 179
Generalized version of method of multiple scales, applications of 276—302
Generalized version of method of multiple scales, description of 232 241—243
Generalized version of method of multiple scales, limitations of 302—303
Generating function 181 184 189 190 192 195 196 200 202 215
Generating vector 201
Geometrical optics 308 361 374—377 379
Geophysics 110
Graetz problem 384
Green's function 362 364 380
Green's function, double 364
Group velocity 179 219 220 267 299
Hamilton — Jacobi equation 181 182 183 186 190 199
Hamiltonian 223 224 225
Hamiltonian for Duffing equation 182
Hamiltonian for Mathieu equation 184
Hamiltonian for swinging spring 186
Hamiltonian, definition of 180
Hamiltonian, transformation of, using Lie transforms 202 212—216
Hamiltonian, transformation of, using von Zeipel procedure 189—200
Harmonic balance 218
Harmonic resonance 219—221 234 262—269
Harmonic wave 76
Heat 45 79 84 156 342 384
Heat, problem for, equation 150—152
Helmholtz equation 234
Hill's equation 60
Hopf equation 381
Hydraulic jump 89
Hyperbolic equation 37 42 57 99 379.
Inclined plane see Flow down
Indicial equation 311
Induction 13
Infinite domain, as a source, of nonuniformity 23—31 229
Infinite domain, as a source, of uniformity 38 42
Inhomogeneous 361
Inhomogeneous, problems with turning points 352—359
Initial, boundary value problem for heat equation 150—152
Initial, layer 23
Inner and our expansions see Matched asymptotic expansions method
Inner expansion 110 112 114 119 145 146 148
Inner expansion for bending of plates 129—132
Inner expansion for earth-moon-spaceship problem 139
Inner expansion for equation with variable coefficients 122—124
Inner expansion for simple example 117—118
Inner expansion for slider bearing 127
Inner expansion for thermoelastic waves 134—135
Inner expansion for turning point problems 336
Inner expansion, definition 117—118
Inner limit 112 118 119 129 131 139
Inner region 113 122 146 153
Inner solution 112 113
Inner variables 119 120 121 144 149 153 154
Inner variables, choice of 114—116 122—124 126—127 134—135 137—138
Inner variables, generalized 145
Instability 78 269.
integral 10 11 12
Integral of motion 24 199
Integral, differential equation 18
Integral, equation 370 380
Integral, relations 99
Intermediate limit 119
Intermediate matching see Overlapping
Jacobi elliptic functions 189
Jacobian matrix 202
Jerky oscillations 34
Jordan, form 327
Jordan, matrix 327
Josephson tunnel 221
Kamel's algorithm 171
Kamel's method 224
Kelvin — Helmholtz 77 235
Kernel 370
Kiylov — Bogolinbov, method of 165—168
Klein — Gordon equation 175 234
Klein — Gordon equation, exercises involving 105 226
Klein — Gordon equation, treated, by averaging using Lagrangian 221—222
Klein — Gordon equation, treated, by Krylov — Bogoliubov — Mitropolski method 178—179
Klein — Gordon equation, treated, by method of multiple scales 301—302
Klein — Gordon equation, treated, by method of strained parameters 76—77
Kruskal's technique 168 191
Krylov — Bogoliubov technique 165—168 223
Krylov — Bogoliubov — Mitropolski technique 174—179 183 194 211 212 223 224 246 248 303
Lagrange equations 179 180
Lagrangian 179
Lagrangian for Bretherton's equations 217
Lagrangian for Klein — Gordon equation 221
Lagrangian for swinging spring 186
Lagrangian, averaging using 216—222 301
Lame coefficients of elasticity 45 90
Laminar 39 54
Landau, equation 382
Landau, symbols 8 9
Langer's transformation 308 346 384
Langer's transformation for first-order turning point problems 339—341
Langer's transformation for generalization of 341—342
Langer's transformation, successive 350
Latta's technique 144—154
Layer 23 79 111;
Libration points see Stability of elliptic triangular points
Lie series and transforms 171 199 200—216 223 225 303
Lie triangle 205 206
Lighthill's technique 57 77—95
Lighthill's technique, exercises involving 107 108
Lighthill's technique, limitations of 79 98—100 107 109
LIMIT 7
Limit, cycle, point, or solution 35 99 109
Limit, distinguished 336
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå