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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 |
Friction coefficient 52 288
Galilean invariance 6
Gamma function 262
Gardner, R.B. 599
Gasdynainic-shallow water analogy 371
Gasdynamic equations 370 392
Gauss’s theorem 332
General solution of a nonlinear first order ODE 77
Generalized coordinates 98 102
Generalized Euler — Lagrange system 504
Generalized momenta 101 102
Generalized symmetries 447
Generate Infinitesimal Table 598
Generate Variable Table 597
Generating function of a Lie contact transformation 454
Geometry of turbulent fine scales 432
Gibbs equation 66 92
Gladkov, A.V. 269 275
Glezer, A. 363 413 415 420 444
Global parameter 401
Goldschmidt, H, L. 599
Goldstein, H. 97 120
Gore, L. 54
Gravitational constant 35 115 125
Green, P.B. 31
Griffiths, P.A. 599
Group 4 9 10 13
Group Blasius equation 219
Group boundary layer stream function equation 301
Group compressible Euler equations 367
Group dilation 18 39 126 133
Group discrete 10 125
Group infinitesimal form 127
Group invariants 129
Group of the Kepler system 116
Group once-extended 15
Group one-parameter 13
Group operator 10 132 152 162 164 178 202 212
Group operator canonical coordinates 163
Group operator definition 128 129
Group operator dilation group 133 151
Group operator diverging channel flow 327
Group operator family of ellipses 165
Group operator Lie — Backlund 450 462
Group operator p-times extended 202
Group operator projective group 135
Group operator prolonged 200 245 450
Group operator rotation group 133 149
Group operator translation group 134
Group parameter 13 122 123 124 127 240
Group point 56 237
Group projective 135
Group reconstruction of the finite form 132
Group rotations in 2D SO(2) 7 131 133 149 153
Group rotations in 3D SO(3) 148 505
Group rotations once extended 225
Group space-time translations 505
Group translation 17 122 134 160
Group translation, equivalence 464
Group unsteady boundary layer equations 302
Hamel, G. 362
Hamilton — Jacobi equation 83 105 106 119
Hamilton — Jacobi equation relation to contact groups 457
Hamiltonian 98 108
Hamiltonian damped oscillator 116 118
Hamiltonian definition 102
Hamiltonian Hamiltonian system 68 104 107
Hamiltonian Hamilton’s equations 101
Hamiltonian Hamilton’s principle 98
Hamiltonian two body problem 101
Hamiltonian undamped harmonic oscillator 102
Hansen, A.G. 3 31
Harmonic oscillator forced 120
Harmonic oscillator undamped 102
Harmonic oscillator unforced 12 97 108
Harrison, B.K. 3 31
Hawkins, T xl
Hayes, B. 173 177
Heat capacities 68 370
Heat conduction nonlinear 293 314
Heat equation 18 248
Heat equation classical group 252
Heat equation commutator table 253
Heat equation determining equations 251
Heat equation invariance condition 251
Heat equation Lie algebra 253
Heat equation nonclassical point group 270
Heat equation recursion operator 479
Heat equation source solution 257
Heat equation source solution modified problem 263
Heaviside function 263
Helgason, S xl
Helical group 146 176
Hereman, W 4 32 585 600
Hermite polynomials 260
Hexagonal group 9
Hidden symmetries 272 324 521 549
Higher order ODEs 213
Homentropic flow 370 392
Homogeneous and isotropic turbulence 419
Hopf, E. 530 550
Hui, W.H. 303 317
Hunt, K.H. 173 177
Hussain, F. 445
Hydon, P. 3 32 233 236 272 276
Hydrodynamic impulse 330 332 334 415
Hyperbolic group 146 176
Hyperbolic trajectory, Kepler problem 114
Hypergeometric functions 261
Ibragimov, N.H. 3 26 31 32 185 190 236 237 274 275 315 317 364 369 393 447 497 551 583
Ideal gas 67
Ideal gas equation of state 67
Ideal gas universal gas constant 67
Ideal Lie subalgebra 139
Identity element 10 13 122 124 127 130
Impulse integral 330 to 336
Impulse integral compressible 393
Impulsively started jet 335
Impulsively started jet compressible started jet 393
Incompressible Euler equations 320
Incompressible flow 73 318
Incompressible Navier — Stokes equations 30 180 313 318 361
Inertial subrange 410 532
Infinite dimensional group 302
Infinite order structure 447
Infinitesimal form of a Lie group 26
Infinitesimal of a group, definition 127
Infinitesimal operator of a group 129
Infinitesimal transformations of derivatives in the plane, formulae 198 199
Infinitesimal transformations of partial derivatives, formulae 243 244
Integrability condition 58 516
Integral length scale 399 403
Integral momentum flux 402
Integral of the motion of a Hamillonian system 103 457
Integral velocity scale 399 403
Integrating factor 60 62 65 66 72 118 131 155 156 159 161 162 166 176 177
Integro-differential recursion operators 486
Internal energy 65 68 370
Intro To Symmetry 29 203 513 524 584 589
Intro To Symmetry applied to Blasius equation 221
Intro To Symmetry applied to buoyancy-induced boundary layers 316
Intro To Symmetry applied to Burgers equation 487
Intro To Symmetry applied to Burgers potential equation 482
Intro To Symmetry applied to compressible viscous flow equations 393
Intro To Symmetry applied to contact transformation 455
Intro To Symmetry applied to Falkner — Skan boundary layers 305
Intro To Symmetry applied to force-free convection equation 275
Intro To Symmetry applied to fourth order PDE 513
Intro To Symmetry applied to gasdynamic equations 392
Intro To Symmetry applied to heat equation 252 255
| Intro To Symmetry applied to incompressible Navier — Stokes equations 319
Intro To Symmetry applied to incompressible sink flow 327
Intro To Symmetry applied to Kepler system 475 512
Intro To Symmetry applied to nonclassical symmetries 272
Intro To Symmetry applied to nonlinear 2nd order ODEs 225 234 235
Intro To Symmetry applied to nonlinear heat equation 274
Intro To Symmetry multivariate polynomial procedure 210
Intro To Symmetry restricted Eulcr equation 442
Intro To Symmetry second order PDE 496
Intro To Symmetry simple linear 2nd order ODE 209
Intro To Symmetry steady boundary layer stream function equation 301
Intro To Symmetry transonic equation 392
Intro To Symmetry unsteady boundary layer stream function equation 317
Intro To Symmetry velocity gradient transport equation 443
Invariance Coadition Rules Applied 598
Invariance condition for differential functions 463 464
Invariance condition for ODEs 202 203 206 207
Invariance condition for PDEs 247
Invariance Condition No Rules 598
Invariance definition 4 127
Invariance infinitesimal condition for 128 129
Invariance of a family of curves 152 153
Invariance of a family of ellipses 165
Invariance of a family of parabolas 126
Invariance of a family of solutions 225 228
Invariance of a function 14 15 125 126
Invariance of boundary conditions 19 282 286
Invariance of contact conditions 200 245 558
Invariant family 149 152 153 155 159 161 162 163 217
Invariant function 14 125
Invariant manifold 168
Invariant points 132
Invariant solution curses 166 168
Invariant solutions of a PDE 255
Invariants of a group 129
Invariants of a matrix 84 85 88 168
Inverse 10 122 125
Inverse square law 112 474 506
Inverse total differentiation operator 555
Invertible map 13 179 188 193 446
Inviseid compressible flow 147 365
Involutory matrix 434
Irreversible process 67
Irrotational field 72 73
Irrotational flow 73 280 303 313
Isentropic flow 369
Isentropic flow of a monatomic gas 369 374
Jackson, J.D. 333 363
Jacobi elliptic functions 170
Jacobi identity 104 137 145
Jacobian 59
Jeffery — Hamel flow 325 329 336 361
Jeffery, G.B. 362
Jeong, J. 445
Jet space 24 129 446
Jets 405
Jones, R.T. 389 394
Jordan algebra 144
Jordan identity 144
Jump conditions across a shock wave 377
Kadomisev, V.V. 551
Kant 1 xli
Kaptsov, O.V. 31 393
Kells, L.M. 74 95
Kepler first law 34 114
Kepler problem 34 112 474 506
Kepler second law 34 111
Kepler system 113 116 474 512
Kepler third law 34 37 38 478
Kepler, Johannes 34
Kestin, J. 73 93 95
Kim, J. 445
Kinematic pressure 319
Kinematic viscosity 320 339
kinetic energy 505 507
Klein — Gordon equation 517
Klein, F. xli
Kolmogorov length and velocity scales 410 411
Kolmogorov, A.N. 409 410 444
Kompaneets, A.S. 315 317
Korteweg de Vries equation 533
Korteweg de Vries equation Backlund transformation 541
Korteweg de Vries equation exact solution 541
Korteweg de Vries equation non-local group 534
Korteweg de Vries equation point group 493
Korteweg de Vries equation potential equation, nonlocal group 534 549
Korteweg de Vries equation potential equation, nonlocal group Backlund transformation for 539
Korteweg de Vries equation potential equation, nonlocal group elementary solution 540
Korteweg de Vries equation potential equation, nonlocal group nonlocal group 535 538
Korteweg de Vries equation potential equation, nonlocal group point group 535
Korteweg de Vries equation recursion operator 490
Korteweg de Vries equation single hump solution 543 544
Korteweg de Vries equation solitary wave solution 533
Korteweg, D.J. 533 550
Kumei, S. 3 31 142 148 219 236 324 362 447 479 497
Kutta condition 304
Lagerstrom, P. 69 95
Lagrange and Charpit method of 74 106 157
Lagrange method of 70 82
Lagrangian 108 101 110 499
Lagrangian Foucaull pendulum 119
Lagrangian two body problem 111
Lagrangian unforced oscillator 100
Lamb, Jr.G. L. 534 550
Laminar boundary layer 277
Laminar line vortex 441
Laminar mixing layer 397
Landahl, M. 394
Landau — Squire jet solution 341 342 344
Landau, L.D. 97 120 310 317 329 362 339 363 341 514
Laplace’s equation 275 303
Laplace’s vector 510
Laplacian 332
Large eddy length scale 399
Lateral correlation function 419
Latus rectum 114
Law of composition 124
Lee, T.D. 6 32
Legendre transformation 65 66 119 456
Leighton, R.B. 32
Lele, S.K. 236
Lie algebra definition 136
Lie algorithm 4 29 247 584
Lie contact transformation 453 570
Lie derivative 129
Lie group definition 123 124
Lie group definition once extended 15
Lie group definition working definition 13
Lie point group 56 237
Lie series 525 537
Lie series expansion of a PDE 247
Lie series expansion of an ODE 201
Lie series expansion of differential functions 462
Lie series representation of a function 128 129
Lie Sophus 139
Lie subalgebra 138
Lie subalgebra Abelian 139
Lie subalgebra Abelian ideal 139
Lie subalgebra Abelian solvable 139 157
Lie — Backlund extended group 461
Lie — Backlund finite, reconstruction of 452
Lie — Backlund group 35 179 446 499 570
Lie — Backlund infinite order structure 569
Lie — Backlund infinitesimal form 449
Lie — Backlund Kepler system 508
Lie — Backlund operator 450 452
Lie — Backlund proper transformation 462
Lie — Backlund transformation 446 448
Lie, S xli
Liepmann, H.W. xix 394
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