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| Cantwell B.J., Crighton D.G. (Ed), Ablowitz M.J. (Ed) — Introduction to Symmetry Analysis |
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| Предметный указатель |
Lifshitz, E.M. 97 120 310 317 329 362 514
Lighthill, M.J. 95
Linear flows in three dimensions 88
Linear flows in two dimensions 85
Liouville equation 517
Liouville equation cross derivative form 517
Lorentz group 146 206
Lorentz transformation 6 12
Lumley, J.I. 444
Ma, P.K.H 303 317
Mach number 46 47 385
Magee, C.J. 550
Magnetostatics analogy 333
Mahalingham, S. 273 275
Make Commutator Table 599
Make Rules Array 598
Mansour, N. 444 445
Mars atmosphere 42
Matrix invariants 84 85 88 340 345 429
Matrix inverse 242 434
McLachtan, B.G. 53 54
McMahon, T.A. 51 54
Meleshko, S.V 375 394
Method of canonical coordinates 215
Method of differential invariants 216 222 226 230 310
Method of Lagrange 70 82 204
Method of Lagrange and Charpit 74
Method of variation of parameters 228
Miller, D.G. 46 48 54
Miura transformation 541
Miura, R.M. 541 551
Mixing layer 397
Moftat, H.K. 329 362
Momenta generalized 101
Monatomic gas 374 392
Moser, R.D. 427 430 444 445
Multi-parameter group 134 157 217
Multipole expansion 333
Navier — Stokes equations 30 318 393
Navier — Stokes equations invariant groups 319
Navier — Stokes equations microscales 419
Newton’s law 96
Nieuwstadt, F.T.M. 550
Nodal point 348
Noether symmety 504
Noether, A.E. 498 513
Noether’s theorem 119 504 513
Non-abelian 9
Non-classical symmetries 269
Non-local group 515 521 528
Non-local group Burgers equation 527
Non-local group KdV potential equation 535 538
Non-uniform translation group 319 320
Nonlinear critical points 87
Nonlinear diffusion 293
Nonlinear eigenvalue problem 266
Nonlinear superposition law for the KdV equation 546
Nonlinear superposition law for the sine-Gordon equation 521 546
Nonlinear wave equation 275 534
Notation 15 23 24 101 178 181 183 240 250
Notation for “dimensions of” 35
Null algebra 136
Null element 144
Nussbaum, A. 30 32
Oberlack, M. 443 445
Olver, P. 3 31 447 479 497
Once-extended finite group 193 239
Once-extended infinitesimal group 197 242
One parameter shear flows 401
One parameter shear flows table of 408
One-parameter Lie group 13 123
One-parameter Lie group definition of 123
Orbit 113 115
Orbital period 115
Ordinary differential equations 191 203
Ordinary differential equations first order 57 62 121 191 203
Ordinary differential equations higher order 221
Ordinary differential equations second order linear 209
Ordinary differential equations second order, nonlinear 225 234 235
Orthogonal functions 262
Oswatitsch, K. 95
Overdamped 117
Ovsiannikov, L.V. 3 31 364 369 393
Parabolic cylinder functions 262 268
Partial differential equations 237
Partial differential equations fourth order 513
Partial differential equations linear, first order 55 57 61 70 121
Partial differential equations nonlinear, first order 74 82
Partial differential equations second order 496
Particle path equations 339 351 404 441
Particle path equations in similarity coordinates 404
Particle path equations in three dimensions 69
Particle path equations in two dimensions 68
Particle path equations Landau — Squire jet 337 338 344
Particle path equations low Reynolds number jet 346
Particle path equations turbulent vortex ring 418
Particle path equations unsteady dipole 345
Pathline of a group 122
Pendulum, simple 93
Pendulum, spherical 119
Perfect differential 57 60 63 80
Perigee 114
Perihelion 115
Permeability 263
Permutahility theorem 521
Perry, A.E. 95 445
Perturbation velocity potential 386
Petviashvili, V.I. 551
Pfaffian 1-form 58 72 155 168
Pfaff’s theorem 59 66 73 157
Phase plane analysis 85 284 287
Phase portrait 83 287 318
Phase portrait bifurcation 330 349
Phase portrait impulsively started jet 348 349 350
Phase portrait turbulent vortex ring 418
Phase space 83 293 318
Plane laminar jet 361 438
Plane mixing layer 396 406
Plane turbulent jet 402 438
Planets, table of 36
Point explosion 375
Point symmetry, point group, point transformation 56 178 185 237
Poisson brackets 103 104
Poisson equation 74 331
Poisson equation for pressure 353
Pollack, J. 54
Porosity 263
Porous medium 264
potential energy 110
Potential equation 521
Potential function 60 385 523
Power monomial function 48
Prandtl — Glauert rule 389
Pressure 42 44 63
Pressure coefficient 384 385 390
Pressure distribution 384 386
Pressure far field 334
Principle of least action 98 99
Production of turbulent kinetic energy 400
Projective group 135 137 145 208
Prolongation 200
Prolonged group 200 245 558 562
Prolonged group operator 200 245 558 563
Prolonged versus extended group 200
Proper Lie — Backlund symmetry 462 486 494
Pthinfinitesimal 597
Pukhnachov, V.V. 31 323 362 393
Quadratic discriminant 85 117
Quadrature, integration by 57 62 63 156 162 230
Quarter chord point 304
| Racing shell 51
Radial vorticity function 344
Raizer, Y.P. 375 394
Rale-of-roialion 426
Rate-ot-strain 426
Ratio of specific heats 382
Rational root, elliptic curve 173 177 349 353 356
Recursion operators 478
Recursion operators Burgers equation 486
Recursion operators Burgers potential equation 481 497
Recursion operators heat equation 479
Recursion operators integro-differential 486
Recursion operators KdV equation 490
Reduced mass 110
Reflection 8
Reflectional symmetry 9
Reid, G.J. 599
Remoissenet, M. 534 547 550
Rennich, S.C. 31
Restricted Euler equation 432 442
Reversible process 67
Reynolds averaged Navier — Stokes equations 398 399
Reynolds decomposition 397
Reynolds number boundary layer 279 284 329
Reynolds number Burgers equation 523
Reynolds number circular Couette flow 330
Reynolds number Falkner — Skan sink flow 308
Reynolds number flow past a circular cylinder 42 43 53
Reynolds number flow past a sphere, compressible 45 48
Reynolds number flow past a sphere, incompressible 41
Reynolds number incompressible flow 318
Reynolds number invariance 395 397 400 401
Reynolds number invariance group interpretation 401
Reynolds number Jeffrey — Hamel flow 326
Reynolds number round jet 335 336 339 343 346 348
Reynolds number scaling 407
Reynolds number Taylor microseale 414 420
Reynolds number turbulent vortex ring 413 419
Reynolds stresses 398
Reynolds, O. 397 444
Reynolds, W.C. 427 445
Ribet, K.A. 173 177
Ricatti equation 120 204 213 232
Ricatti equation solution 205
Rodionov, A.A. 31 393
Rogers, C. 3 31 516 550
Rogers, M.M. 427 430 444 445
Roshko, A.R. xix 394 396 444
Rotation group 7
Rotation group in 2D once extended 225
Rotation group in three dimensions, SO(3) 148 505
Rotation group in two dimensions, SO(2) 7 131 133 149 153
Rotation invariants 434
Rott, N. 445
Runge — Kutta 132 147
Runge — Lenz vector 510
Saddle 86 288 296 348 417
Saffman, P. 332 363 394
Sagan, C. 54
Sands, M. 32
Schoppa, W. 445
Schwarz, F. 32
Scott, A.C. 550
Second order ODE invariant under a given group 213
Second order ODEs, table of 214
Second Term 597
Sedov, L.I. 375 394
Segev, M. 534 550
Semenova, I.B. 362
Series solution of the determining equations 209 251
Shallow water approximation 371
Shock wave 45 375
Shu, D. 53 54
Similarity rules 395 403
Similarity rules, inertial subrange 411
Similarity rules, vortex ring 416
Similarity variables 19
Similarity variables Blasius boundary layer 282
Similarity variables diverging channel flow 326
Similarity variables Falkner — Skan boundary layers 307 357
Similarity variables Falkner — Skan sink flow 308
Similarity variables heat equation 19 20 260
Similarity variables homentropic equations 372
Similarity variables nonlinear diffusion equation 294
Similarity variables spherical blast wave 380
Similarity variables turbulent vortex ring 417
Similarity variables unsteady round jet 338
Sine-Gordon equation 519 521
Single hump solution, KdV equation 543
Singular solution 77 79
Skan, S.W. 317
Skin friction coefficient 52 288
Snook, K. 54
Sobel, D. xli
Solitary wave Korteweg de Vries equation 533
Solitary wave sine-Gordon equation 521
Soliton 521
Solvable Lie algebra 139 140 141 142 217 233
Solvable Lie algebra definition 140
Solve Determining Equations 210 252 255 584 585 593 594 595 596 597 599
Sondergaard, R. 95 444 445
Soria, J. 95 430 445
Source point 13 14 127 132
Source space 188 192 240 454 570
Space of differential functions 185
Spalart, P.R. 445
Spatial similarity rules 405
Sphere drag 38 41 44 46 47 48
Sphere drag low Re 41
Spherical blast wave 375
Spreiter, J.R. 394
Squire, H.B. 339 341 362 363
Stable focus 288 417 418
Stanaway, S.K. 445
Starting vortex 330 335
State-space analysis 83 318
Steele, C.S 31
Stegeman, G. 534 550
Stegun, I.A. 262 275
Stekctee, J.A. 550
Stephani, H. 3 24 31 59 95 234 236 497 514
Stillwell, J. xli 88 95
Stokes creeping jet 343 347
Stokes equations 30
Stokes stream function 336 337 341 343
Strain invariants 434
Stream function 60 68 74 280 323
Stream function equation 323
string variables 597
Stronge, W.J. 53 54
Structure constants of a Lie algebra 136
Structure constants of a vector space 142
Sturm — Liouville equation 260
Subalgebra 138
Subalgebra Abelian 139
Subalgebra ideal 139
Subalgebra solvable 139 157
Subgroup 10 138
Subsonic flow 386
Subsonic similarity 388
Substantial derivative 185 555
Superposition principle for linear equations 161
Supersonic flow 389
Supersonic similarity 389
Suzuki, T. 236
Symmetry analysis software 584
Symmetry and beauty 2
Symmetry continuous 12
Symmetry definition 4
Symmetry discrete 4 10
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