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| Karman T., Biot A.M. — Mathematical Methods in Engineering |
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| Ïðåäìåòíûé óêàçàòåëü |
Law, of areas 77
Law, of conservation of energy 91 93
Law, of inertia 70
Law, of motion, Newton's 70—71
Legendre's polynomials 69
Legendre's standard form of elliptic integrals of first kind 121
Lift, of airplane 144 250
Limit, of function 472
Limit, of sequence 470
Linear difference equations 439—442
Linear differential equations, fundamental system of solution of 37
Linear differential equations, general theorems 35—37
Linear differential equations, homogeneous 23 35—37
Linear differential equations, of first order 22—24
Linear differential equations, of higher order 37—40
Linear differential equations, of second order 24—26 31—34
Linear differential equations, oscillatory solutions of 311—313
Linear differential equations, self-adjoint 312—313
Linear differential equations, solution of, by use of operators 368
Linear differential equations, system of 41—42
Linear equations, homogeneous 471—472
Linear equations, nonhomogeneous 471—472
Linear transformation of coordinates 184—186
Load diagram, of electric machines 370
Logarithm 469
Logarithm, common or Briggs 469
Logarithm, natural or Napierian 469
Logarithmic decrement 130—132
Longitudinal stability, of airplane 249—255
Low-pass filter 463 465—467
Lubrication, problem from theory of 44—45
Magnetic energy 232
Mass center (center of gravity) 78—80
Mass, impedance of 373—374
Matrix 196—202 208—209 472
Matrix, column 199
Matrix, square 199 472
Maxwell's theorem 191
Mechanical chain 461—464
Mechanical chain as model of electric wave filter 463—465
Mechanical chain, length of waves in 462
Mechanical chain, progressing wave in 461—464
Mechanical chain, velocity of propagation in 462
Mechanical impedance 374 376—378
Mechanical methods for harmonic analysis 339—340
Mechanical-electrical analogy 228—233 372—377
Membrane, equilibrium of 359—362
Membrane, free oscillation of 315—317
Membrane, Rayleigh — Ritz method applied to 359—362
Microphone, condenser 256 436
Modes, normal, calculation of, by matrices 196—204 208—209
Modes, of buckling 297
Modes, of oscillation, fundamental 169
Modes, of oscillation, normal 176—178 187—191
Modes, of oscillation, of beams 287—288 291
Modes, of oscillation, of strings 284—285
Modes, of oscillation, principal 169 172
Modes, of vibration (see "Modes of
Modified Bessel functions 61—62
Modulus, of elastic foundation 271
Modulus, of elliptic integral of first kind 121
Modulus, of vector 367
Moment, bending 268
Moment, gyroscopic 88—89
Moment, of aerodynamic forces on airplane 223—224 249—251
Moment, of force 75—76
Moment, of inertia 85
Moment, of inertia, of areas 270
Moment, of inertia, principal 85
Moment, of momentum 76
Moment, of momentum, rate of change of 77—78
Moment, of momentum, resultant 78
Moment, of precession 88—89
Moment, twisting 268
Momentum 71
Momentum, generalized 104—106
Momentum, rate of change of 71 78
Momentum, resultant 78
Motion in resisting medium 111—113
Motion of particle under gravity and air resistance 139—143
Motion of pendulum 115—119 126—128
Motion of rigid body 82—85
Motion of rigid body, around fixed point 84—89
Motion, of single mass point 74—77
Motion, oscillatory, damped 131—132
Motion, phugoid, of airplane 145—150
Motion, plane 83—84
Motion, quantity of 70
Motion, relative 82
Motion, simple harmonic 115
Motion, subsident 131—133
Motion, with elastic restraint 114—115
Motion, with elastic restraint, and damping 130—132
Motion, with elastic restraint, under periodic force 132—139
Multicylinder engine, critical speed of 453—461
Multiple roots, of algebraic equation 471
Multiple roots, of characteristic equation 38—39
Multiple-valued function 470
Napierian logarithm 469
Natural frequencies, identified with characteristic values 311—314
Natural frequencies, of beams 286 293
Natural frequencies, of coupled masses 168
Natural frequencies, of strings 284—286
Natural logarithm 469
Negative integer 469
Network (see "Electric networks")
Neumann's function 63—64
Neutral equilibrium of column 297
Newton's laws of motion 70—71
Newton's laws of motion, application of, to system 77—78
Newton's method, extension of, to complex roots 248—249
Newton's method, for algebraic equations 192—193
Nodal point 152—153 155 157
Nonconservative force 91
Nonconservative systems, oscillations of 217—220
Nonhomogeneous boundary conditions 310
Nonhomogeneous boundary problems 310
Nonhomogeneous differential equations 259—260
Nonhomogeneous linear differential equations 33 35—37 40
Nonhomogeneous linear equations 471—472
Nonperiodic phenomena, application of Fourier integral to 388—394
Normal components of force 189
Normal coordinates of mechanical systems 183—186
Normal modes of oscillation 176—178 187—191
Normal modes, calculation of, by matrices 196—204 208—209
Normal modes, coefficients of 177—180
Normal modes, static deflection of 190
Normalization, of principal oscillations 176—178
Normalizing condition 177—178
Number, algebraic 471
Number, complex 469
Number, imaginary 469
Number, irrational 469
Number, rational 469
Number, real 469
Number, transcendental 471
Numerical methods, for evaluation of integrals 3—6
Numerical methods, for harmonic analysis 336—338
Numerical solution of differential equations 14—19
Nutation of vertical top 238
Ohmic resistance 229
Operational calculus 409—434
Operational calculus, applied to oscillations of mechanical systems 423—430
Operational calculus, expansion methods of 416—420
Operational rules 407 411—416
Operators 368
Operators, addition of 411
Operators, expansion in partial fractions of 417—420
Operators, fundamental 414—416
Operators, multiplication of 430—433
| Operators, notion of 409—411
Ordinary differential equation, defined 474
Orthogonal functions 351—353
Orthogonality of principal oscillations 172—176
Orthogonality relation 173 176 209
Oscillating systems, stability conditions of 242—246
Oscillations, damped 131—132
Oscillations, forced 186—191
Oscillations, forced, damped 137—139
Oscillations, forced, of cantilever beam 294—295
Oscillations, forced, of elastically restrained mass 379—380
Oscillations, forced, undamped 133—136
Oscillations, free, of membrane 315—317
Oscillations, fundamental mode of 169
Oscillations, harmonic, reduced to statical problem 283—284
Oscillations, linear, of coupled masses 166—170
Oscillations, normal modes of 176—178 187—191
Oscillations, of beams 286—295
Oscillations, of beams, carrying a mass 290—294
Oscillations, of cantilever beam 288—290
Oscillations, of coupled masses 166—170
Oscillations, of crankshaft 454—461
Oscillations, of electric circuit 369
Oscillations, of hinged beam 286—288
Oscillations, of nonconservative systems 217—220
Oscillations, principal 169 172
Oscillations, principal modes of 169 172
Oscillations, principal, amplitudes of 177
Oscillations, principal, determined by operational calculus 423—430
Oscillations, principal, kinetic energy of 180—186
Oscillations, principal, normalization of 176—178
Oscillations, principal, potential energy of 180—186
Oscillations, small, of conservative systems 162—166
Oscillations, steady state 365 388
Oscillations, with increasing amplitude 136—137
Oscillatory solutions of linear differential equations 311—313
overtones 285
Parametric form for equation of curve 476
Partial derivatives of function 473
Partial differential equation, denned 474
Pendulum, compound 115
Pendulum, counterweight 159
Pendulum, double 204—207
Pendulum, gyroscopic 242
Pendulum, motion of 115—119 126—128
Perfect differential 91
Perfect electromagnetic coupling 372
Period of simple harmonic motion 115
Periodic force, response to 382—385
Periodic force, vectorial representation of 367—368
Periodic motions, phenomena 385
Periodic motions, superposition of 378—382
Periodic motions, voltage impressed on electric circuit 380—382 385
Phase angle 366
Phase lag 138
Phase, of vector 367
Phugoid motion of airplane 145—150 253
Pipe, under internal pressure 274—277
Plane motion 83—84
Plasticity, problem from theory of 45
Polar coordinates 105
Polynomial of nth degree 470
Polynomials, Legendre's 69
Positive definite, quadratic form 164
potential energy 90
Potential energy of principal oscillations 180—186
Potential energy, external 92—93
Potential energy, internal 92—93 98
Power series 471
Power series, inversion of 293—294
Precession 87—89
Precession of vertical top 238
Precession, free 87
Precession, moment of 88—89
Principal axis of ellipse 184—186
Principal flexural rigidity 270
Principal inertia axis, of area 270
Principal modes of oscillation 169
Principal moment of inertia 85
Principal oscillations 169 172
Principal oscillations, amplitudes of 177
Principal oscillations, determined by operational calculus 423—430
Principal oscillations, kinetic energy of 180—186
Principal oscillations, normalization of 176—178
Principal oscillations, orthogonality of 172 176
Principal oscillations, potential energy of 180—186
Principal part of difference of function 473
Principal value of integral 475
Principle of superposition 378—379 388 403
Product, of areas 270
Product, of inertia 85
Product, scalar 72—74
Product, vector 72—74
Progressing wave in mechanical chain 461—464
Progression, arithmetic 439
Progression, geometric 439
Quadratic form 164
Quadratic form, positive definite 164
Quadrature 2
Quantity of motion 70
Quartic algebraic equations, stability conditions for 244—246
Radius vector 75
Rational number 469
Rayleigh — Ritz method 353—362
Rayleigh — Ritz method, deflection of membrane, determined by 359—362
Rayleigh — Ritz method, determination of buckling load by 358—359
Rayleigh — Ritz method, determination of critical speed by 354—357
Reactions 94—95
Reactions, frictionless 95
Reactions, internal 94—95
Real number 469
Real part of complex number 469
Real roots of algebraic equations 191—196
Reciprocity theorem of elastic systems 191
Rectangular coordinates, defined 475
Rectilinear coordinates, defined 475
Relative motion 82
Resistance, ohmic 229
resistor 229
Resistor, impedance of 370 374
Resonance 132—139 295 311 349—351 377
Resonance factor 134 190 349 351
Response, of elastically restrained mass, to unit impulse 399
Response, of electric circuit to unit impulse 400—401
Response, of electric network to suddenly applied voltage 420—423
Response, of force, spectrum of 390—392
Response, of mechanical system to suddenly applied force 423—430
Response, of system to force 389—392
Response, relation of, to indicial admittance 401—403
Response, static, of system to unit force 419
Response, to periodic force 382—385
Response, to unit impulse 397—403 404—405 415—416
Response, to unit step (see "Indicial admittance")
Restoring force 164—165
Rigid body 82—85
Rigid body, kinetic energy of 93—94
Rigid body, motion of, around fixed point 84—89
Rigid body, rotation of 84
Ritz method (see "Rayleigh — Ritz method")
Rotating shaft, critical speed of 286 290
Rotation of rigid body 84
Rule, Simpson's 4
Rule, Simpson's, trapezoidal 4
Runge — Kutta method 14 18—19
Saddle point 149 153—157
Saw-toothed function, Fourier series for 383—384
Scalar product 72—73
Scalar quantities 71
Self-adjoint linear differential equations 312—313
Semiconvergent series for Bessel functions of zero order 54
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