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| Karman T., Biot A.M. — Mathematical Methods in Engineering |
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| Ïðåäìåòíûé óêàçàòåëü |
Double pendulum 204—207
Drag of airplane 144 250
Driving point impedance 371—372
Duhamel's integral 403—405
Dynamic balance, of aileron 228
Dynamic coupling 166
Dynamic spring constant 376—378
Dynamic spring constant of flywheel 456—457
Dynamic stability, of airplane 252—255
Dynamically coupled systems 204—210
Dynamically coupled systems, frequency equation of 208
Elastic axis of airplane wing 221
Elastic foundation, beams on 271—273
Elastic foundation, modulus of 271
Elastic mounting of airplane engine 212
Elastic restoring force 114
Elastic systems, influence coefficient of 190—191
Elastic systems, reciprocity theorem of 191
Elastically supported beam, buckling of 304—306
Elastically supported strings 266—267
Electric circuits, electromagnetic coupling of 372
Electric circuits, impedance of 370—371
Electric circuits, oscillations of 369
Electric coil 229
Electric coil, impedance of 370 374
Electric current, vectorial representation of 369—370
Electric insulators, voltage drop of 451—453
Electric machines, equivalent network of 372 386
Electric machines, load diagram of 370
Electric networks, dissipation function of 232—233
Electric networks, equivalent 229—232
Electric networks, equivalent of electric wave filter 465—466
Electric networks, equivalent of string insulator 452
Electric networks, impedance of 370—372 375—376
Electric networks, ladder type 376—378
Electric networks, Lagrange's equations for 232—233
Electric networks, response of to suddenly applied alternating voltage 433—434
Electric networks, response of to suddenly applied voltage 420—423
Electric transformer, equivalent network of 372 386
Electric wave filter 463—467
Electrical-mechanical analogy 228—233 372—374
Electromagnetic coupling, of electric circuits 372
Electromagnetic coupling, perfect 372
Electromotive force 229—231
Electromotive force vectorial representation of 369—370
Electrostatic energy 232
Elliptic functions, Jacobi's 125—126
Elliptic integrals 118—130
Elliptic integrals of first kind 118 120—126
Elliptic integrals of first kind, complete 126
Elliptic integrals of first kind, Legendre's standard form of 121
Elliptic integrals of first kind, standard form of 123—125
Elliptic integrals of second kind 128—129
Elliptic integrals of second kind, complete 128
Elliptic integrals of third kind 129
Energy, electrostatic 232
Energy, kinetic 90
Energy, kinetic of rigid body 93—94
Energy, law of conservation of 91
Energy, magnetic 232
Energy, method 352—362
Energy, potential 90
Energy, wandering of 170
Envelope of family of curves 13—14
Equation, of curve 475
Equation, of plane 475
Equation, of straight line 476
Equation, of surface 475
Equations of motion, aerial bomb 140—143
Equations of motion, airplane 143—145
Equations of motion, Lagrange's 101—106
Equations of motion, rigid body 82—85
Equations of motion, single mass point 74—77
Equations of motion, system of mass points 77—82
Equilibrium of systems 95—98
Equilibrium, stability of 97—98 164
Equivalent network 229—232
Equivalent network of electric machine 372 386
Equivalent network of transformer 372 386
Euler's equation for motion of rigid body 85
Euler's formula for buckling 299
Expansion f operators in partial fractions 417—420
Expansion theorems of operational calculus 416—420
Exponential functions, with imaginary exponent 25—26
External forces 77—78
Factor, damping 132
Factor, damping, critical 132
Factor, integrating 12
Factor, resonance 134 190 349 351
Factorial function 57
Factorization of algebraic equations 247—248
Finite differences, calculus of 437—439
First integral of differential equations 21—22 113
Flexural rigidity, of beams 269
Flexural rigidity, principal 270
Flight path of airplane 145—150
Flutter of airplane wings 220—228
Flywheel, dynamic spring constant of 456—459
Force, central 77
Force, centrifugal 82 101
Force, conservative 90—91
Force, Coriolis 82 220
Force, damping 218—220
Force, diagram 263
Force, elastic restoring 114 130
Force, external 77—78
Force, generalized 102—103
Force, gyroscopic 220
Force, inertia 98
Force, internal 77—78
Force, nonconservative 91
Force, normal components of 189
Force, periodic, motion of particle under 132—139
Force, restoring 164—165
Force, shear 268
Force, suddenly applied to mechanical system 423—430
Force-displacement impedance 374
Force-velocity, impedance 374
Forced oscillations 133—139 186—191
Forced oscillations of beams 347—352
Forced oscillations of beams, cantilever 294—295
Forced oscillations of elastically restrained mass 379—380
Forced oscillations, damped 137—139
Forced oscillations, undamped 133—136
Forced oscillations, vibrations 133—139 186—191
Fourier coefficients 325—327
Fourier coefficients, complex 385
Fourier coefficients, integral 343—347
Fourier coefficients, integral, applied, to indicial admittance 405—407
Fourier coefficients, integral, applied, to nonperiodic phenomena 388—394
Fourier coefficients, integral, inversion of 390—391
Fourier coefficients, integral, theorem 345
Fourier coefficients, integral, theorem, complex form of 390
Fourier coefficients, integral, transition from Fourier series 389—390
Fourier series 325—335
Fourier series for saw-toothed function 383—384
Fourier series of discontinuous functions 327—330 335
Fourier series, applied to forced vibration of beam 347—352
Fourier series, approximation of arbitrary functions by 330—335
Fourier series, complex form of 384—385
Fourier series, Dirichlet's condition for convergence of 334
Fourier series, transition to Fourier integral 389—390
Frequency equation, of crankshaft 458—461
Frequency equation, of dynamically coupled system 208
Frequency equation, of statically coupled system 171
Frequency equation, solution of, by matrices 196—202
Frequency, cut-off, of wave filters 463—467
Frequency, natural, of coupled masses 168
Frequency, of simple harmonic motion 115
Friction, coefficient of 95
| Friction, reactions 95
Function, continuous 472
Function, differentiable 473
Function, multiple-valued 470
Function, single-valued 470
Fundamental mode, of oscillation 169
Fundamental system, of solutions 37
Fundamental tone 285
Generalized coordinate 101
Generalized force 103
Generalized momentum 104—106
Generalized velocity 102
Geometric progression 439
Geometrical constraints 94—97
Governor, stability of 258
Graeffe's method, for algebraic equations 194—196
Graphical methods, for harmonic analysis 388—339
Graphical representation, of bending moments 263 309
Gyroscope 85—89
Gyroscope, applications of 88
Gyroscope, symmetrical 86—89
Gyroscopic force 220
Gyroscopic moment 88—89
Gyroscopic pendulum 242
Hankel functions, of arbitrary order 59
Hankel functions, of imaginary argument 63
Hankel functions, of zero order 54
Harmonic analysis 335—340
Harmonic analysis, graphical methods for 338—339
Harmonic analysis, mechanical methods for 339—340
Harmonic analysis, numerical methods for 336—338
Harmonic components of force 391
Harmonic components, continuous spectrum of 392
Harmonic oscillation of string 284—286
Harmonic oscillation, amplitude of 283
Harmonic oscillation, reduced to statical problem 283—284
Harmonic oscillation, vibration 283
Harmonics 285
Heat exchange, problems of 321—322
Heat transfer, problem from theory of 44
Heaviside operational calculus 409—410
High-pass filter 466—467
Hinge moment 223
Hinged beam, oscillation of 286—288
Hinged support, of beams 269
Hodograph 141—142
Homogeneous boundary conditions 310
Homogeneous boundary conditions, problems of 310
homogeneous differential equations 10 259—260
Homogeneous differential equations, associated 33 35—37
Homogeneous differential equations, characteristic values of 311—317
Homogeneous linear equations 471—472
Hydraulic jump 161
Hyperbolic functions 27—30
Hyperbolic integrals 120
Hyperbolic inverse 120
Identity 470
Imaginary number 469
Imaginary part of complex number 469
Impedance 365 370—378 389—390 405—410
Impedance in parallel 375—376
Impedance in series 375—376
Impedance of capacitor 370 374
Impedance of circuit 370
Impedance of dashpot 373 374
Impedance of electric coil 370 374
Impedance of electric network 370—372 375—376
Impedance of inductance 370
Impedance of mass 373—374
Impedance of mechanical system 373—374 376—378
Impedance of resistor 370 374
Impedance of spring 373—374
Impedance, driving point 371—372
Impedance, force-displacement 374
Impedance, force-velocity 374
Impedance, total 371
Impedance, transfer 372 422—423
Implicit equation 474
Improper integral 392 395 405—407 475
Increment of variable 473
Indefinite integral 474
Indicial admittance 397—434
Indicial admittance of clastieally restrained mass 897—398
Indicial admittance of electric circuit 399—400
Indicial admittance, application of Fourier integrals to 405—407
Indicial admittance, relation of, in response to unit impulse 401—403
Inductance, coefficients 232
Inductance, coefficients of coil 229
Inductance, coefficients, impedance of 370
Inertia parameter 165
Inertia, axis 85 270
Inertia, force 98
Inertia, law of 70
Inertia, moment of 85
Inertia, product of 85
Infinite sequence 470
Infinite series 470
Infinite series, convergence of 470—471
Infinite series, sum of 470
Infinite trigonometric series 471
Influence coefficients of elastic system 190—191
Influence function of strings 265—267
Initial conditions 22
Integer, negative 469
Integral calculus 1
Integral numbers 469
Integral, Bromwich's 405—407
Integral, circular 120
Integral, curve 2
Integral, definite 1 474
Integral, Dirichlet's 395
Integral, Duhamel's 403—405
Integral, elliptic 118—130
Integral, elliptic of first kind 118 120—126
Integral, elliptic of second kind 128—129
Integral, elliptic of third kind 129—130
Integral, equation, Carson's 407—409
Integral, first, of differential equations 21—22 113
Integral, Fourier 343—347
Integral, Fourier, complex form of 390—392
Integral, hyperbolic 120
Integral, improper 475
Integral, improper, principal value of 475
Integral, indefinite 474
Integral, numerical evaluation of 3—6
Integrating factor 12
Internal forces 77—78
Internal reactions 94—95
Inverse circular functions 120
Inverse hyperbolic functions 120
Inversion, of Fourier integral 390—391
Inversion, of power series 293—294
Irrational number 469
Isocline 7
Isocline method 7
Iteration method, for algebraic equations 193—194
Iteration method, for determining characteristic values 313—317
Jacobi's elliptic functions 126
Kepler's first law 77
kinetic energy 90
Kinetic energy of principal oscillations 180—186
Kinetic energy of rigid body 93—94
Ladder-type electric network 376 378
Lagrange's equations 101—106
Lagrange's equations for dissipative systems 220 232
Lagrange's equations for electric networks 232—233
Lagrangian function 106
Laplace transform 409 430—432
Lattice truss, buckling, of 445—451
Law, of action and reaction 71
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