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Karman T., Biot A.M. Ч Mathematical Methods in Engineering
Karman T., Biot A.M. Ч Mathematical Methods in Engineering

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Ќазвание: Mathematical Methods in Engineering

јвторы: Karman T., Biot A.M.

язык: en

–убрика: “ехнологи€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1940

 оличество страниц: 505

ƒобавлена в каталог: 26.03.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Adams' method      14Ч19
Aerodynamic forces on airplane      143Ч145 222Ч224 249Ч251
Affine transformation      156
Aileron, dynamic balance of      228
Aileron, effect of      223
Aileron, static balance of      227
Air resistance, motion of particle with      139Ч143
Air resistance, of bombs      160
Airplane wing, axial and lateral load acting on      306Ч309
Airplane, aerodynamic forces on      143Ч145 222Ч224 249Ч251
Airplane, damping parameter of      252 255
Airplane, drag of      144 249Ч250
Airplane, dynamic stability of      249Ч255
Airplane, equations of motion of      143Ч145
Airplane, flight path of      145Ч150
Airplane, lift of      144 250
Airplane, longitudinal stability of      249Ч255
Airplane, moment of aerodynamic forces on      144 223Ч224 249Ч251
Airplane, phugoid motion of      145Ч150 253
Airplane, small oscillations of      250Ч255
Airplane, stability parameter of      252Ч255
Airplane, static stability of      252Ч255
Airplane, wing flutter of      220Ч228
Algebraic equations      471
Algebraic equations, biquadratic      226Ч227 242
Algebraic equations, complex roots of      246Ч249
Algebraic equations, cubic, stability conditions for      242Ч243
Algebraic equations, factorization of      247Ч248
Algebraic equations, Gfaeffe's method for      194Ч196
Algebraic equations, iteration method for      193Ч194
Algebraic equations, Newton's method for      192Ч193
Algebraic equations, quartie, stability conditions for      244Ч246
Algebraic equations, real roots of      191Ч193
Algebraic equations, roots of      471
Algebraic equations, solution of      191Ч196
Algebraic equations, squaring roots of      194Ч196
Algebraic equations, test function for      244Ч247
Algebraic number      471
Algebraic operations      471
Alternating current, vectorial representation of      369Ч370
Alternating voltage, suddenly applied to electric network      433Ч434
Amplitude of elliptic integral of the first kind      121 125
Amplitude of harmonic vibration, of strings and beams      283
Amplitude of principal oscillations      177 190 191
Amplitude of simple harmonic motion      115 134
Amplitude, distribution of harmonic components      390Ч397
Analogy of electrical and mechanical systems      228Ч233 372Ч374
Analyzer, differential      19
Angular frequency of simple harmonic motion      115
Angular velocity      74
Apparent mass      222
Argument of vector      367
Arithmetic progression      439
Associated homogeneous differential equation      33 35Ч37
Asymptotic approximation for Bessel functions      51Ч54 58Ч59 62
Axial thrust      268
Ballistic problem      139Ч143
Band-pass filter      463Ч467
Beams      267Ч309
Beams, bending of      267Ч270
Beams, cantilever, vibration of      288Ч290
Beams, carrying mass, vibration of      290Ч294
Beams, clamped support of      269
Beams, curvature of      268Ч269
Beams, deflection of      271
Beams, elastically supported, bending of      271Ч273
Beams, elastically supported, buckling of      304Ч306
Beams, elastically supported, solution by Fourier series      323Ч325 340Ч343
Beams, flexural rigidity of      269
Beams, forced vibration of      347Ч352
Beams, free end of      269
Beams, hinged, support of      269
Beams, hinged, vibration of      286Ч288
Beams, of infinite span, solution by Fourier integral      343Ч347
Beams, torsional rigidity of      270
Beams, vibration of      286Ч295
Beats      136 170
Bending moment      268
Bending moment, graphical representation of, by string polygon      263
Bending moment, graphical representation of, for combined loading      309
Bending, of beams      267Ч270
Bessel functions      47Ч68
Bessel functions of first kind of arbitrary order      57Ч58
Bessel functions of first kind of zero order      49
Bessel functions of half an odd integer order      60Ч61
Bessel functions of higher order      55Ч56
Bessel functions of imaginary argument      63
Bessel functions of negative order      58
Bessel functions of second kind of arbitrary order      58Ч59
Bessel functions of second kind of zero order      50
Bessel functions of second kind, Weber's form      58 63Ч64
Bessel functions of third kind of arbitrary order      59
Bessel functions of third kind of zero order      54
Bessel functions of zero order      47Ч54
Bessel functions, modified      61Ч62
Bessel functions, of zero order, asymptotic approximations      52Ч54
Bessel functions, semi-convergent series, for      54
Bessel functions, special properties of      60Ч61
Bessel functions, standard forms of      56Ч59
Bessel functions, table of symbols      64
Bessel's differential equation      47
Bessel's differential equation of zero order      47Ч54
Bessel's differential equation, equivalent forms of      64Ч68
Binomial coefficients      438
Biquadratic algebraic equation      225Ч227 242
Bombs, air resistance of      160
Borel's theorem      430Ч433
boundary conditions      22
Boundary conditions for clamped support of beams      269
Boundary conditions for difference equations      443Ч445 458
Boundary conditions for free end of beams      269
Boundary conditions for hinged support of beams      269
Boundary conditions of differential equations      259Ч260
Boundary conditions, homogeneous      310
Boundary conditions, nonhomogeneous      310
Boundary problems      309Ч313
Boundary problems, homogeneous      310
Boundary problems, nonhomogeneous      310
Briggs's logarithm      469
Bromwich's integral      405Ч407
Buckling loads, determination of, by energy method      358Ч359
Buckling loads, identified with characteristic values      311
Buckling of lattice truss      445Ч451
Buckling of tapered columns      299Ч301
Buckling of uniform columns      295Ч299
Buckling, Euler'is formula for      299
Buckling, modes of      297
Buckling, of columns      295Ч304
Buckling, of columns, under own weight      301 304
Cable tension, of suspension bridge      278 281Ч283
Cantilever beam, forced vibration of      294Ч295
Cantilever beam, free vibration of      288Ч290
Capacitor      229
Capacitor, impedance of      370 374
Capacity of condenser      229
Carson's integral equation      407Ч409
Cartesian coordinates, denned      475
Catenary      9Ч10
Center of gravity (mass center)      78Ч80
Center of percussion      207
Central force      77
Centrifugal force      82 101
Chain, mechanical      461Ч464
Chain, of electrical insulators      451Ч453
Characteristic equation, multiple roots of      38Ч39
Characteristic equation, of coupled system      374
Characteristic equation, of linear differential equations      24 31 38 41
Characteristic exponents of coupled system      374
Characteristic values, applied, to buckling      311
Characteristic values, applied, to critical speeds      311Ч314
Characteristic values, applied, to free vibrations      311Ч314
Characteristic values, determination of, by energy method      352Ч359
Characteristic values, determination of, by iteration method      313Ч317
Characteristic values, of differential equations      260
Characteristic values, of homogeneous differential equations      311Ч317
Circular functions      28
Circular functions, inverse      120
Circular integrals      120
Clamped support of beams      269
Coefficient of friction      95
Coefficients, inductance      232
Coefficients, of capacitance      232
Coefficients, of normal modes      177Ч180
Coil, electric      229
Coil, impedance of      370Ч374
Column matrix      199
Column, buckling of      295Ч304
Column, buckling of, under own weight      301Ч304
Column, critical load of      297
Column, neutral equilibrium of      297
Column, stability of      297Ч299
Column, tapered, buckling of      299Ч301
Column, uniform, buckling of      295Ч299
Combined loading, graphical representation of bending moment of      309
Combined loading, of airplane wing      306Ч309
Common logarithm      469
Complex exponentials      25 366
Complex form of Fourier integral theorem      390
Complex Fourier coefficient formula      385
Complex Fourier series      384Ч385 389
Complex number      469
Complex number, imaginary part of      469
Complex number, real part of      469
Complex quantities, vectorial representation of      366Ч370
Complex roots, extension of Newton's method to      248Ч249
Complex roots, of algebraic equations      246Ч249
Condenser microphone      256 436
Condenser, capacity of      229
Conservative forces      90Ч91
Conservative systems      162Ч166
Conservative systems, with dynamic coupling      204Ч210
Constraints, geometrical      94Ч97
Continued fraction      376
Continuous beams, difference equations applied to      442Ч445
Continuous beams, three-moment equation for      442Ч443
Continuous function      472
Continuous spectrum of harmonic components      392
Convergence, of Fourier series, Dirichlet's condition for      334
Convergence, of infinite series      470Ч471
Convergence, uniform, of infinite series      471
Cooling fin      321
Coordinates, Cartesian, defined      475
Coordinates, generalized      101
Coordinates, normal, of mechanical systems      183Ч186
Coordinates, polar      105
Coordinates, rectangular, defined      475
Coordinates, rectilinear, defined      475
Coordinates, transformation of      184Ч186
Coriolis force      82 220
Coupled masses, oscillation of      166Ч170
Coupled systems      162Ч255 370Ч378
Coupled systems, characteristic equation of      374
Coupled systems, characteristic exponents of      374
Coupled systems, frequency equation of      171 208
Coupling, dynamic      166 204Ч210
Coupling, static      165Ч166
Crankshaft, frequency equation for      458Ч461
Crankshaft, oscillations of      454Ч461
Critical damping      132
Critical factor      132
Critical load, of column      297
Critical speed of multicylinder engine      453Ч461
Critical speed of rotating shaft      286 290
Critical speed of rotating shaft, determination of, by energy method      354Ч357
Critical speed of rotating shaft, determination of, by iteration method      313Ч314
Critical speed, identified with characteristic values      311Ч314
Cubic algebraic equations, stability conditions for      242Ч244
Curvature of beams      268
Cut-off frequency of wave filters      463Ч467
D'Alembert's principle      98Ч101
Damped oscillations      131Ч132
Damped systems      130Ч132
Damper, vibration      233Ч237
Damping      218Ч220 229
Damping factor      130Ч132
Damping factor, critical      132
Damping forces      218Ч220
Damping parameter of airplane      252 255
Damping, critical      132
Dash pot      130 230
Dash pot, impedance of      373Ч374
Decrement, logarithmic      132
Definite integral, defined      474
Deflection, of beams      271
Deflection, of strings      260Ч267
Derivative, of function      473
Derivative, partial, of function      473
Determinant      472
Difference equations      437Ч468
Difference equations applied, to buckling of truss      445Ч451
Difference equations applied, to continuous beams      442Ч445
Difference equations applied, to critical speeds of multicylinder engine      453Ч461
Difference equations applied, to electric wave filters      465Ч467
Difference equations applied, to voltage drop in chain of insulators      451Ч453
Difference equations applied, to waves in mechanical chain      461Ч465
Difference equations, boundary conditions for      443Ч445 458
Difference equations, linear, theory of      439Ч442
Difference, of function      473
Difference, of function, principal part of      473
Difference, of order n      438
Differential analyzer      19
Differential equation of first order      6Ч14
Differential equation of higher order      19Ч22
Differential equation, associated homogeneous      33 35Ч37
Differential equation, Bessel's      47
Differential equation, Bessel's of zero order      47Ч54
Differential equation, boundary conditions of      259Ч260
Differential equation, characteristic values of      260
Differential equation, first integral of      21Ч22 113
Differential equation, homogeneous      10 259Ч260
Differential equation, homogeneous, characteristic values of      311Ч317
Differential equation, linear of higher order      37Ч40
Differential equation, linear of second order      21Ч22 24Ч26 31Ч34
Differential equation, linear, general theorems      35Ч37
Differential equation, linear, homogeneous      23 35Ч37
Differential equation, linear, nonhomogeneous      33 35Ч37
Differential equation, linear, of first order      11Ч13 22Ч24
Differential equation, linear, oscillatory solutions of      311Ч313
Differential equation, linear, self-adjoint      312Ч313
Differential equation, linear, system of      41Ч42
Differential equation, nonhomogeneous      259Ч260
Differential equation, numerical solution of      14Ч19
Differential equation, ordinary, defined      474
Differential equation, partial, defined      474
Differential equation, particular      3 13Ч14 33Ч42
Differential equation, singular      13Ч14
Differential equation, singular points of      148Ч157
Differential equation, solution, general      3 9 20 24 32Ч33 3GЧ42
Differential, of function      473
Differential, perfect      91
Differentiate function      473
Dirichlet's, condition for convergence of Fourier series      334
Dirichlet's, integral      395
Discontinuity, finite, of function      473
Displacements, virtual      94Ч98
Dissipation function      218Ч219
Dissipation function of electric networks      232Ч233
Dissipative systems, Lagrange's equation for      220 232
Divergence, torsional      223
Divergent infinite series      470
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