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| Авторизация |
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| Belotserkovsky S.M., Lifanov I.K. — Method of Discrete Vortices |
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| Предметный указатель |
Fredholm equations of second kind 181
Fredholm equations,elasticity theory and 362 -363
Fredholm equations,integrodifferential equations and 239
Fredholm equations,segments and 154
Fredholm’s theory of constructing 155
Free vortices 247
Free vortices,blunt body aerodynamics and 340
Free vortices,circulation of 304
Free vortices,discrete 304
Free vortices,jumping across airfoil surface by 358
Free vortices,strengths of 304
Free vortices,velocity of 318
Friction 14
Gamma functions theory 132
Gases,density of 7
Gases,dynamics of 8
Gases,energy dissipation of 8
Gases,flow of 7
Gases,moving in 8
Gases,pressure of 7
Gases,unperturbed flow of 7
Gases,unperturbed speed of 9
Gases,velocity of 7
Gaussian quadrature formulas 410
Generalized functions theory 374
Generalized polynomials 208
Grid points 21
Grid points,equally spaced 112
Grid points,unequally spaced 113
Grids 23
Hadamard criterion 146
Hadamard finite value 24
Harmonic function 327
Heat conduction law 370
Heat conductivity 371
Heat generation 370
Helmholtz equation 388
Helmholtz equation,Dirichlet and Neumann problems for 404—414
Helmholtz equation,Dirichlet and Neumann problems for,formulation of 404—408
Helmholtz equation,Dirichlet and Neumann problems for,model problems in 408—411
Hilbert’s kernel 4
Hilbert’s kernel,boundary value problems and 422
Hilbert’s kernel,elasticity theory and 363
Hilbert’s kernel,equations on circles with 182—190
Hilbert’s kernel,singular integral equations with 199—203
Hilbert’s kernel,singular integral equations with,of first kind 422
Hilbert’s kernel,singular integral equations with,variable coefficients and 212—215
Hilbert’s kernel,singular integrals over circles with 345
Hilbert’s kernel,singular integrals with 57—58
Hilbert’s Problem 4
Hilbert’s transform 397
History of singular integral equations 2—7
Holder conditions 30
Holder functions 208
Holder-continuous functions 398
Horseshoe vortices,blunt body aerodynamics and 323
Horseshoe vortices,discrete 284
Horseshoe vortices,oblique 249
Horseshoe vortices,slanting 293
Horseshoe vortices,straight 255
Horseshoe vortices,usual 254
Hydrodynamics 6
Improper integral 2
Incompressible fluids 14
Inertia see "Virtual inertia"
Infinite discontinuities 343
Infinite-span vortex filament 249
Infinite-span wings 160
Influence functions 374
Integrable singularities 6
Integral equations see "Singular integral equations"
Integrals 10
Integrals,Abel 309
Integrals,Bernoulli 14
Integrals,Cauchy see "Cauchy integrals"
Integrals,Cauchy principal value of 3
Integrals,Cauchy — Lagrange 247
Integrals,divergent improper 2
Integrals,improper 2
Integrals,invariant 14
Integrals,multiple Cauchy see "Multiple singular Cauchy integrals"
Integrals,singular see "Singular integrals"
Integrals,two-dimensional 24
Integrodifferential equations 239—241
Integrodifferential equations in blunt body aerodynamics 324—327
Integrodifferential equations,Prandtl 58
Integrodifferential equations,two-dimensional 239
Internal point of the frame 75
Interpolation polynomial 399
Invariant integral 14
Inversion formulas 224
Inviscid compressible gas 7
Inviscid incompressible fluid 245
Irrotational flow 7
Iterated kernels 157
Jacobi polynomials 194
Jacobian 89
Jet hydrodynamics 6
Jordan’s two-dimensional measure 104
Joukowski airfoils 13
Joukowski theorem 247
Karman vortex street 430
Kernels,Cauchy 4
Kernels,continuous 155
Kernels,Hilbert’s see "Hilberl’s kernel"
Kernels,iterated 157
Kinematic viscosity 15
Kolosov — Muskhelishvili formulas 361
Korneichuk inequality 70
Lame equations 372
Laplace equation 246
Laplace equation in boundary value problems 388
Laplace equation,Dirichlet and Neumann problems for 421—423
Leading edge 13
Leading edge of canonic trapezoids 299
Leading edge of trapezoids 296
Leading edge,equations for 300
Leading edge,two-dimensional airfoil problems and 260
Left-hand direct product 233
Lift 8
Lift of thin airfoils 1
Lift,coefficients of 15
Lift,maximum 8
Lift-generating structural elements 7
Lifting surface 21
Linear multipliers 194
Linear steady problems of aerodynamics 25
Linear unsteady problems 303—309
lines 29
Liouville theorem 6
Local flow velocity 342
Local shock waves 15
Local sound speed 9
Local supersonic zone 14
Locally polytropic processes 8
Logarithmic singularities 419 421
Lord Kelvin condition 337
Lyapunov contour 38
Lyapunov curves 24
Lyapunov curves,closed 39
Lyapunov curves,elasticity theory and 363
Lyapunov curves,nonintersecting 39
Lyapunov curves,open 51
Lyapunov curves,piecewise 52
Lyapunov curves,unclosed 51
Mach number 9
Mapping 18
Mass conservation law 8
Mass ejection 10
Maximum flight speed 15
| Maximum lift 8
Maxwell equations 415
Meixner conditions 405
Metric of the space of functions 211
Minimum drag 8
Modified Bessel equation 391
Momentum conservation 8
Multi-dimensional singular integrals 24
Multi-dimensional singular integrals,quadrature formulas for 103—110
Multiple singular Cauchy integrals 24
Multiple singular Cauchy integrals on products of plane curves 224
Multiple singular Cauchy integrals,analytical solutions to 217—224
Multiple singular Cauchy integrals,defined 32
Multiple singular Cauchy integrals,integrodifferential equations and 239— 241
Multiple singular Cauchy integrals,inversion formulas for 224
Multiple singular Cauchy integrals,numerical solutions for 224—239
Multiple singular Cauchy integrals,numerical solutions for,canonic division and 229
Multiple singular Cauchy integrals,numerical solutions for,common multipliers and 227
Multiple singular Cauchy integrals,numerical solutions for,Cramer rule and 226
Multiple singular Cauchy integrals,numerical solutions for,uniform grids and 233
Multiple singular Cauchy integrals,numerical solutions for,unit-radius circles and 224
Multiple singular Cauchy integrals,of second kind 234
Multiple singular Cauchy integrals,one-dimensional 82
Multiple singular Cauchy integrals,Poincare — Bertrand formula and 120—124
Multiple singular Cauchy integrals,quadrature formulas and 75—83
Multiple singular integrals 24
Multiple singular integrals for finite-span wings 96—103
Multiple singular integrals in aerodynamics 83—92
Multiple singular integrals,Cauchy see "Multiple singular Cauchy integrals"
Multiple singular integrals,quadrature formulas for 92—95
Multipliers 83
Muskhelishvili equations 363
n-dimensional torus 80
Natural regularizing factors 345
Neumann problem 412—417 also
No-circulation flow 261
No-penetration boundary conditions 259
No-penetration condition 245
No-penetration condition,blunt body aerodynamics and 324
No-penetration condition,three-dimensional airfoil problems and 284
No-penetration condition,two-dimensional airfoil problems and 279
No-penetration condition,wake 320
No-slip condition 245
Node of curves 32
Node vicinity 53
Noncirculatory flow 22
Noncirculatory flow,blunt body aerodynamics and 338
Noncirculatory flow,three-dimensional airfoil problems and 298
Nonintersecting Lyapunov curves 39
Nonintersecting segments 56
Nonintersecting smooth closed curves 217
Nonlinear unsteady problems 316—322
Nonpenetration condition 11
Nonsingular nodes 204
Nonzero total circulation 22
Numerical integration see "Quadrature"
Oblique horseshoe vortices 249
One-dimensional Cauchy integrals 102
One-dimensional singular integrals 29 60
One-dimensional singular integrals of first kind 217
One-dimensional singular integrals on circles 66—69
One-dimensional singular integrals on segments 39—51
One-dimensional singular integrals on segments,theorems for 42— 48
One-dimensional singular integrals over closed contours 32—39
One-dimensional singular integrals over piecewise smooth curves 51—56
One-dimensional singular integrals with Hilbert’s kernel 57—58
One-dimensional singular integrals,Cauchy 77
One-dimensional singular integrals,defined 29—32
One-dimensional singular integrals,Poincare — Bertrand formula and 115—120
One-dimensional singular integrals,theory of 29—32
Open curves 51
Optimal airfoil 1
Optimal flight speed 15
Oscillating wings 288
Outer force 7
Parachutes 281
Perfect incompressible fluid 83
Permeable airfoils 281—282
Perturbed flow 8
Piecewise Lyapunov curves 52
Piecewise smooth curves 30
Piecewise smooth curves,singular integral equations on 203 -211
Piecewise smooth curves,singular integrals over 51—56
Plane curves 224
Plane strain 361
Plane stress 361
Poincare — Bertrand formula 24 124
Poincare — Bertrand formula,full equation on segments and 157
Poincare — Bertrand formula,multiple singular Cauchy integrals and 120—124
Poincare — Bertrand formula,one-dimensional singular integrals and 115—120
Poincare — Bertrand formula,singular integral equations on segments and 136
Poincare — Bertrand formula,validity of 119
Poisson coefficient 385
POLYGONS 249
Polynomials 429
Polynomials,Chebyshev 24
Polynomials,generalized 208
Polynomials,interpolation 399
Polynomials,Jacobi 194
Polynomials,trigonometric 202
Polytropic processes 8
Potential 13
Power-law integrable discontinuities 426
Prandtl equation 58
Prandtl vortex 321
Pressure 15
Pressure,contact 369
Pressure,decrease in 379
Pressure,distribution of 341
Pressure,gas 7
Pressure,gas flow 8
Quadrangular-triangular vortices 330
Quadrature formulas 24
Quadrature formulas for multi-dimensional singular integrals 103—110
Quadrature formulas for multiple Cauchy integrals 75—83
Quadrature formulas for multiple singular integrals 92—95
Quadrature formulas for singular integrals for finite-span wings 96—103
Quadrature formulas for singular integrals in aerodynamics 83—92
Quadrature formulas for singular integrals on circles 66—69
Quadrature formulas for singular integrals on segments 39—51
Quadrature formulas for singular integrals over closed contours 32—39
Quadrature formulas for singular integrals over piecewise smooth curves 51—56
Quadrature formulas for singular integrals with Hilbert’s kernel 57—58
Quadrature formulas for singular integrals,estimation of 346
Quadrature formulas for singular integrals,multiple Cauchy integrals and 75—83
Quadrature formulas for singular integrals,theorems for 42—48
Quadrature formulas,coefficients of 429
Quadrature formulas,construction of 426
Quadrature formulas,Gaussian 410
Quadrature formulas,regularizing factors and 350
Quadrature formulas,theory of 29— 32
Quadrature formulas,unification of difference formulas and 58—60
Radiation 405
Rectangle rule formulas 180
Rectangles 54
Rectangular vortices 255
Rectangular wings,finite-span 239
Rectangular wings,flow with circulation past 283—288
Rectangular wings,flow without circulation past 288 -293
Rectilinear vortex segments 249
Reference points 21
Reference points,elasticity theory and 368
Reference points,three-dimensional airfoil problems and 284
Reference points,two-dimensional airfoil problems and 76
Reference points,velocity component at 304
Regularizing factors 135
Regularizing factors for singular integral equations 350—357
Regularizing factors in unsteady aerodynamic problems 357—358
Regularizing factors,natural 345
Regularizing factors,self- 345
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