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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 |
Abelian group 9 10 123 124
Abelian Lie algebra 139
Abramowitz, M. 262 275
Acceleration field 353
Acceleration field gradient 354
action 99 105
Action integral 99 105 499 500
Action of a harmonic oscillator 108
Affine transformation 85
Aksenov, A.V. 275
Allen, G.A. 363
Alternating unit tensor 59
Ames, W.F. 3 31 516 550
Analytic function 128 129 185
Anderson, R.L. 3 31 447 497 513 550 569 570 583
Andreev, V.K. 3 31 364 393
Apogee 114
Area of an elliptic orbit 115
Ashkenas, H. 394
Ashley, H. 394
Associativity 10 130
Associativity of a Lie group 125
Auto-Backlund transformation 516 549
Autonomous 56
Autonomous infinite order system of ODEs 452
Autonomous pair of ODEs in the plane 55 86 168 287 310
Autonomous particle path system 79 130 338 358 404
Autonomous system of ODEs 125
Axi-symmetric Laplace equation 275
Axially symmetric wave equation 274
Backlund transformations 515
Backlund transformations for Burgers equation 530
Backlund transformations for the KdV equation 541
Backlund transformations for the Liouville equation 517
Backlund transformations sine-Gordon equation 519
Baikov, V.A. 269 275
Bailey, A.B. 46 48 54
Barenblatt, G.I. 3 21 31 32 44 51 54 262 275
Barone, A. 534 550
Bashforth, F.A. 46 47 54
Batchelor, G.K. xix 317 444
Baumann, G. 3 32 272 275 276
Beaupre, G. 54
Bernoulli relation 280 385
Bianchi permutation relation 521 548
Bianchi, L. 521 550
Bifurcation 325 330 335 339 348 352
Binary operation of composition 123
Binomial series 135
Binomial series Blasius 281 439
Binomial series Blasius equation 179 219 278 284 471 596
Binomial series invariant group 219
Binomial series similarity variables 282
Binomial series thermal analogy 299
Birkhoff, G. 3
Birkhoff, G.D. 2 31
Blackburn, H.M. 445
Blaom, A.D. 120
Blasius, H.M. 278 281 317
Blast wave problem 375
Blast wave problem in 2D 392
Bluman, G. 3 31 142 148 219 236 272 276 324 362 447 479 497
Boulton, A. 599
Boundary layers 277
Boundary layers stream function equation 301 305
Boundary layers stream function equation invariant group 301
Boundary layers unsteady 302 316
Boundary layers unsteady invariant group 302
Boundary layers with pressure gradient 301
Boussinesq approximation 315 407
Bradshaw, P. 444
Brahc, Tycho 34
Bridgeman, P.W. 47 54
Browand, F.K. 444
Brown, G.L. 395 444
Bryant, R.L. 599
Buchnev, A.A. 362
Buckingham Pi theorem 12 47 283
Buoyancy induced flow 316
Buoyant jet 440
Burgers equation 180 486
Burgers equation Backlund transformation for 530
Burgers equation Burgers potential equation 22 481
Burgers equation integro-differential operator for 486 522
Burgers equation kinetic energy 548
Burgers equation N wave solution 549
Burgers equation nonlocal group 527 528 548
Burgers equation point group for 482 486
Burgers equation relation to turbulence 530
Burgers equation single hump solution 531
Burgers equation solution 524
Burgers, J.M. 441 445 522 550
Burke — Schumann flame 273
Canonical coordinates 162 163
Canonical coordinates reduction of order by 215
Cantwell, B.J. 54 95 177 362 363 444 445
Cardano formula 89
Cardano formula surface 89
Cardano, Girnlamo 88
Cauchy initial value problem 278 291 294
Cauchy — Riemann conditions 60 92
Central force field 35 111 112 506
Centrifugal energy 513
Chacin, J.M. 445
Chain rule 179 552
Characteristic equations 57 71 81 107 121 130 162 202 206 247 326 338
Characteristic equations Lagrange and Charpit method 74
Characteristic equations Lagrange method 70 82 204
Characteristic function 255 256 451 458
Characteristic surface 80
Characteristics 56 64
Characteristics family of 56
Characteristics in n dimensions 79 81
Chen, J.H. 427 445
Cheng, W.P. 434
Chern, S.S. 599
Chester, W. 3 31
Chong, M.S. 95 445
Chord line 304 385
Chord-tangent construction 173 174
Chorin, A. 444
Circular cylinder drag 42 43
Circular cylinder wake 322
Circulation 441
Clairaut equation 166
Clarkson, P.A. 272 276 551
Closure 9 124 125
Cohen, A. 3 31
Cole — Hopf transformation 529
Cole, J.D. 3 31 272 276 394 530 550
Coles, D. 54 330 362 363 413 415 420 444
Colliding solitons 545
Coloumb gauge 74
Commutator definition 135
Commutator definition table, Blasius equation group 221
Commutator definition table, heat equation group 253
Commutator definition table, projective group 137 138 599
Complete set of orthogonal functions 262
Complete solution 77
Complex lamellar field 73
Complimentary error function 21
Composition of groups 122 123 124 125
Compressible Euler equations 365
Compressible flow 364 549
Confluent hypergeometric functions 261
Conic section 114
Conservation law 119 495 498 504
Conservation of energy 505 507
Conserved integral 258 265 325 334 438
Conserved vector 504
| Constant of the motion 98
Contact between a curve and a surface 552
Contact conditions 187 189 192 245 246 448
Contact conditions first order 187 238
Contact conditions higher order 189
Contact conditions infinite order 448
Contact conditions invariance of 200 201 558
Contact transformation 67 453 496
Continuity equation 30 68 280 323 365
Coordinate independence 11
Covariance principle of 10 11 20 33 39 40
Covariant vector 101
Cox, A.B. 54
Critical points classification in 2D 86
Critical points classification in 3D 89 91
Critical points in a turbulent vortex ring 418
Critical points in the unsteady round jet 344 345 346
Critical points linear 84 88
Critical points nonlinear 87
Critically damped 117
Cubic discriminant 89 168 173 340 427
Cubic equation 88
Curl of a vector 58
Curly brace notation 15 183
Cylindrical coordinates, two body problem 111
Damped, linear second order system 116
Damping coefficient 116
Darboux, G. 521 550
Darcy’s law 263
Daykin, D.E. 53 54
de Vries, G. 533 550
Determining equations 178 209 212 237 248 584 587 591
Determining equations method of solution 130
Deviation function 99
Diffeomorphism 13 23 446
Differentiable manifold 58
Differential 80 552
Differential 1-form 58 60
Differential consequences 463
Differential function 129 178 179 186 499
Differential function definition of 185
Differential variables 185 448
Differential volume 59
Differential volume transformation of 499
Diffusion coefficient 19
Diffusion equation with shearing convection 275
Diffusivity 20 254
Diffusivity of pressure 264
Dilation group 18 39 126 133 158 168
Dilation group blast wave problem 379
Dilation group Clairault equation 166
Dilation group heat equation 18
Dilation group Kepler system 116
Dilation group Navicr — Stokcs equations 30 283 313 320 330 336
Dilation group nonlinear heat equation 293
Dilation group stream function equation 281
Dimension, definition of 33
Dimensional analysis 33 283
Dimensional homogeneity 11 12
Dimotakis, P. 363
Diophantene construction 173 357
Diophantus 173
Dirac delta function 336
Discrete groups 10
Discriminant of a cubic equation 89
Discriminant of a quadratic equation 85
dispersion 533
Dissipation of turbulent kinetic energy 400 419
Diverging channel 325
Dorodnitsyn, V. 32
Drag coefficient 41 47
Drag of a circular cylinder 42 43
Drag of a sphere 38 44 46 47 48
dragging 132
Dual stream function 69
Duffy, B.R. 329 362
D’Alembert’s paradox 304
d’Alembert’s principle 96 97
Earth diameter and mass 35
Eccentricity 35 38 114 510
Eigenvalues of a cubic 90
Eigenvectors 86 296
Einstein derivative notation 24
Einstein summation convention 15 80
Einstein, A. xxxiii xl 24 32
Elliptic curve 172
Elliptic curve 3D flow patterns 353
Elliptic function 170 171
Elliptic integral 170
Elliptical orbit 35 114
Energy dissipation integral 548
Engel, F. xli
Ensemble mean 397
Enthalpy 66 68 92 370
Entrainment velocity 439
entropy 66 67 378
Equation of state 66
Equation of state ideal gas 67 370
Equivalence classes of transformations 457
Ergodic theorem 2
Error function, complimentary 21
Esposito, F 550
Estabrook, F.B. 3 31
Euler equations, compressible 365
Euler equations, incompressible 401
Euler operator 502
Euler — Lagrange equations 97 100 101 498
Exponential map 132
Extended group 15 17 18 178 179 185
Extended Lie — Backlund group 461
Extended Lie — Backlund group in the plane 15 17 183 191
Extended Lie — Backlund group operator 188 202 247
Extended versus prolonged group 200
Exterior differential forms 59
Falkner — Skan boundary layers 305 325 357
Falkner — Skan boundary layers Falkner — Skan equation 307
Falkner — Skan boundary layers sink floss 310 312
Falkner — Skan boundary layers source flow 310
Falkner — Skan boundary layers velocity profiles 308
Falkner, V.M. 317
Falling dominos 52 53
Family of curves 56 131
Family of curves circles 131
Family of curves ellipses 165
Family of curves parabolas 63 457 466
Family of curves solution curves 167
Feynman, R.P. xxxiii xl 4 11 32
Find Determining Equations 209 210 255 584 585 591 593 594 595 597 599
Fine scale motions 408 424
Finite form of a Lie group 132 163
Finite Lie — Backlund transformation 447 449
Finite transformation of first derivatives in the plane 15 193
Finite transformation of first partial derivatives 239
Finite transformation of higher derivatives in the plane 196
Finite transformation of second and higher partial derivatives 239 240
Finite transformation of second derivatives in the plane 195
First order linear ODE in n dimensions 62 160
First order linear PDE in n dimensions 81
First order ODEs 55 57 61 69 149 157 206
First order ODEs table of 158
First order PDEs 55 57 61 70 81
First order PDEs nonlinear 74
Flow in a diverging channel 325
Force free convection equation 275
Forsyth, A.R. 3 31 515 550
Foucault pendulum 119
Frames of reference 321 322 351 362 404
Frames of reference nonuniform translation, compressible flow 549
Frames of reference nonuniform translation, incompressible flow 321
Free shear flows 397
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