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| Karman T., Biot A.M. — Mathematical Methods in Engineering |
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| Ïðåäìåòíûé óêàçàòåëü |
Adams' method 14—19
Aerodynamic forces on airplane 143—145 222—224 249—251
Affine transformation 156
Aileron, dynamic balance of 228
Aileron, effect of 223
Aileron, static balance of 227
Air resistance, motion of particle with 139—143
Air resistance, of bombs 160
Airplane wing, axial and lateral load acting on 306—309
Airplane, aerodynamic forces on 143—145 222—224 249—251
Airplane, damping parameter of 252 255
Airplane, drag of 144 249—250
Airplane, dynamic stability of 249—255
Airplane, equations of motion of 143—145
Airplane, flight path of 145—150
Airplane, lift of 144 250
Airplane, longitudinal stability of 249—255
Airplane, moment of aerodynamic forces on 144 223—224 249—251
Airplane, phugoid motion of 145—150 253
Airplane, small oscillations of 250—255
Airplane, stability parameter of 252—255
Airplane, static stability of 252—255
Airplane, wing flutter of 220—228
Algebraic equations 471
Algebraic equations, biquadratic 226—227 242
Algebraic equations, complex roots of 246—249
Algebraic equations, cubic, stability conditions for 242—243
Algebraic equations, factorization of 247—248
Algebraic equations, Gfaeffe's method for 194—196
Algebraic equations, iteration method for 193—194
Algebraic equations, Newton's method for 192—193
Algebraic equations, quartie, stability conditions for 244—246
Algebraic equations, real roots of 191—193
Algebraic equations, roots of 471
Algebraic equations, solution of 191—196
Algebraic equations, squaring roots of 194—196
Algebraic equations, test function for 244—247
Algebraic number 471
Algebraic operations 471
Alternating current, vectorial representation of 369—370
Alternating voltage, suddenly applied to electric network 433—434
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 390—397
Analogy of electrical and mechanical systems 228—233 372—374
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 35—37
Asymptotic approximation for Bessel functions 51—54 58—59 62
Axial thrust 268
Ballistic problem 139—143
Band-pass filter 463—467
Beams 267—309
Beams, bending of 267—270
Beams, cantilever, vibration of 288—290
Beams, carrying mass, vibration of 290—294
Beams, clamped support of 269
Beams, curvature of 268—269
Beams, deflection of 271
Beams, elastically supported, bending of 271—273
Beams, elastically supported, buckling of 304—306
Beams, elastically supported, solution by Fourier series 323—325 340—343
Beams, flexural rigidity of 269
Beams, forced vibration of 347—352
Beams, free end of 269
Beams, hinged, support of 269
Beams, hinged, vibration of 286—288
Beams, of infinite span, solution by Fourier integral 343—347
Beams, torsional rigidity of 270
Beams, vibration of 286—295
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 267—270
Bessel functions 47—68
Bessel functions of first kind of arbitrary order 57—58
Bessel functions of first kind of zero order 49
Bessel functions of half an odd integer order 60—61
Bessel functions of higher order 55—56
Bessel functions of imaginary argument 63
Bessel functions of negative order 58
Bessel functions of second kind of arbitrary order 58—59
Bessel functions of second kind of zero order 50
Bessel functions of second kind, Weber's form 58 63—64
Bessel functions of third kind of arbitrary order 59
Bessel functions of third kind of zero order 54
Bessel functions of zero order 47—54
Bessel functions, modified 61—62
Bessel functions, of zero order, asymptotic approximations 52—54
Bessel functions, semi-convergent series, for 54
Bessel functions, special properties of 60—61
Bessel functions, standard forms of 56—59
Bessel functions, table of symbols 64
Bessel's differential equation 47
Bessel's differential equation of zero order 47—54
Bessel's differential equation, equivalent forms of 64—68
Binomial coefficients 438
Biquadratic algebraic equation 225—227 242
Bombs, air resistance of 160
Borel's theorem 430—433
boundary conditions 22
Boundary conditions for clamped support of beams 269
Boundary conditions for difference equations 443—445 458
Boundary conditions for free end of beams 269
Boundary conditions for hinged support of beams 269
Boundary conditions of differential equations 259—260
Boundary conditions, homogeneous 310
Boundary conditions, nonhomogeneous 310
Boundary problems 309—313
Boundary problems, homogeneous 310
Boundary problems, nonhomogeneous 310
Briggs's logarithm 469
Bromwich's integral 405—407
Buckling loads, determination of, by energy method 358—359
Buckling loads, identified with characteristic values 311
Buckling of lattice truss 445—451
Buckling of tapered columns 299—301
Buckling of uniform columns 295—299
Buckling, Euler'is formula for 299
Buckling, modes of 297
Buckling, of columns 295—304
Buckling, of columns, under own weight 301 304
Cable tension, of suspension bridge 278 281—283
Cantilever beam, forced vibration of 294—295
Cantilever beam, free vibration of 288—290
Capacitor 229
Capacitor, impedance of 370 374
Capacity of condenser 229
Carson's integral equation 407—409
Cartesian coordinates, denned 475
Catenary 9—10
Center of gravity (mass center) 78—80
Center of percussion 207
Central force 77
Centrifugal force 82 101
Chain, mechanical 461—464
Chain, of electrical insulators 451—453
Characteristic equation, multiple roots of 38—39
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 311—314
| Characteristic values, applied, to free vibrations 311—314
Characteristic values, determination of, by energy method 352—359
Characteristic values, determination of, by iteration method 313—317
Characteristic values, of differential equations 260
Characteristic values, of homogeneous differential equations 311—317
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 177—180
Coil, electric 229
Coil, impedance of 370—374
Column matrix 199
Column, buckling of 295—304
Column, buckling of, under own weight 301—304
Column, critical load of 297
Column, neutral equilibrium of 297
Column, stability of 297—299
Column, tapered, buckling of 299—301
Column, uniform, buckling of 295—299
Combined loading, graphical representation of bending moment of 309
Combined loading, of airplane wing 306—309
Common logarithm 469
Complex exponentials 25 366
Complex form of Fourier integral theorem 390
Complex Fourier coefficient formula 385
Complex Fourier series 384—385 389
Complex number 469
Complex number, imaginary part of 469
Complex number, real part of 469
Complex quantities, vectorial representation of 366—370
Complex roots, extension of Newton's method to 248—249
Complex roots, of algebraic equations 246—249
Condenser microphone 256 436
Condenser, capacity of 229
Conservative forces 90—91
Conservative systems 162—166
Conservative systems, with dynamic coupling 204—210
Constraints, geometrical 94—97
Continued fraction 376
Continuous beams, difference equations applied to 442—445
Continuous beams, three-moment equation for 442—443
Continuous function 472
Continuous spectrum of harmonic components 392
Convergence, of Fourier series, Dirichlet's condition for 334
Convergence, of infinite series 470—471
Convergence, uniform, of infinite series 471
Cooling fin 321
Coordinates, Cartesian, defined 475
Coordinates, generalized 101
Coordinates, normal, of mechanical systems 183—186
Coordinates, polar 105
Coordinates, rectangular, defined 475
Coordinates, rectilinear, defined 475
Coordinates, transformation of 184—186
Coriolis force 82 220
Coupled masses, oscillation of 166—170
Coupled systems 162—255 370—378
Coupled systems, characteristic equation of 374
Coupled systems, characteristic exponents of 374
Coupled systems, frequency equation of 171 208
Coupling, dynamic 166 204—210
Coupling, static 165—166
Crankshaft, frequency equation for 458—461
Crankshaft, oscillations of 454—461
Critical damping 132
Critical factor 132
Critical load, of column 297
Critical speed of multicylinder engine 453—461
Critical speed of rotating shaft 286 290
Critical speed of rotating shaft, determination of, by energy method 354—357
Critical speed of rotating shaft, determination of, by iteration method 313—314
Critical speed, identified with characteristic values 311—314
Cubic algebraic equations, stability conditions for 242—244
Curvature of beams 268
Cut-off frequency of wave filters 463—467
D'Alembert's principle 98—101
Damped oscillations 131—132
Damped systems 130—132
Damper, vibration 233—237
Damping 218—220 229
Damping factor 130—132
Damping factor, critical 132
Damping forces 218—220
Damping parameter of airplane 252 255
Damping, critical 132
Dash pot 130 230
Dash pot, impedance of 373—374
Decrement, logarithmic 132
Definite integral, defined 474
Deflection, of beams 271
Deflection, of strings 260—267
Derivative, of function 473
Derivative, partial, of function 473
Determinant 472
Difference equations 437—468
Difference equations applied, to buckling of truss 445—451
Difference equations applied, to continuous beams 442—445
Difference equations applied, to critical speeds of multicylinder engine 453—461
Difference equations applied, to electric wave filters 465—467
Difference equations applied, to voltage drop in chain of insulators 451—453
Difference equations applied, to waves in mechanical chain 461—465
Difference equations, boundary conditions for 443—445 458
Difference equations, linear, theory of 439—442
Difference, of function 473
Difference, of function, principal part of 473
Difference, of order n 438
Differential analyzer 19
Differential equation of first order 6—14
Differential equation of higher order 19—22
Differential equation, associated homogeneous 33 35—37
Differential equation, Bessel's 47
Differential equation, Bessel's of zero order 47—54
Differential equation, boundary conditions of 259—260
Differential equation, characteristic values of 260
Differential equation, first integral of 21—22 113
Differential equation, homogeneous 10 259—260
Differential equation, homogeneous, characteristic values of 311—317
Differential equation, linear of higher order 37—40
Differential equation, linear of second order 21—22 24—26 31—34
Differential equation, linear, general theorems 35—37
Differential equation, linear, homogeneous 23 35—37
Differential equation, linear, nonhomogeneous 33 35—37
Differential equation, linear, of first order 11—13 22—24
Differential equation, linear, oscillatory solutions of 311—313
Differential equation, linear, self-adjoint 312—313
Differential equation, linear, system of 41—42
Differential equation, nonhomogeneous 259—260
Differential equation, numerical solution of 14—19
Differential equation, ordinary, defined 474
Differential equation, partial, defined 474
Differential equation, particular 3 13—14 33—42
Differential equation, singular 13—14
Differential equation, singular points of 148—157
Differential equation, solution, general 3 9 20 24 32—33 3G—42
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 94—98
Dissipation function 218—219
Dissipation function of electric networks 232—233
Dissipative systems, Lagrange's equation for 220 232
Divergence, torsional 223
Divergent infinite series 470
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