|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Frazer R.A., Duncan W.J., Collar A.R. — Elementary Matrices |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Abbreviated rules for matrix products 8
Absent coordinates see “Ignorable coordinates”
Absolute velocity and acceleration 246
Acceleration derivatives 284
Addition and subtraction of matrices 4
Adjoint matrix, defined 21
Adjoint matrix, derived see “Derived adjoint matrices”
Adjoint matrix, for simple first-order system 205
Adjoint matrix, of characteristic matrix 65 70 73—78
Adjoint matrix, of lambda-matrix 61—64 165—167
Adjoint matrix, of multiply degenerate matrix 21 62 63 65 123 125 173 174
Adjoint matrix, of simply degenerate matrix 21 61 62 63 65 68 76 123 124
Adjoint matrix, of singular matrix 21 121—125 172—175
Aerodynamical derivatives, denned 264
Aerodynamical derivatives, for aeroplane 285 286
Aerodynamical derivatives, for coupled oscillations of aerofoil 385 386 391
Aerodynamical derivatives, generalised 284
Aerodynamical forces, departures of, from linear laws 397
Aerodynamical stiffness 264 284 385
Aerodynamical systems, critical speed for flutter of 291 358
Aerodynamical systems, equilibrium of 264
Aerodynamical systems, forced oscillations of 302—307
Aerodynamical systems, small motions of 283—284
Aerofoil, frictional pitching oscillations of 382—397
Aerofoil, non-frictional pitching oscillations of 397 398
Aeroplane tail, ankylotic motion of 378—379
Aeroplane tail, critical speed for flutter of 359 363
Aeroplane tail, decaying oscillations of 359 361
Aeroplane tail, diagrams relating to flutter of 359 361
Aeroplane tail, influence of friction on flutter of 360 362
Aeroplane tail, steady oscillations of 360—372 375 380
Aeroplane tail, wind tunnel experiments on flutter of 332 333 361
Aeroplane wing, critical speed for flutter of 302 307
Aeroplane wing, forced oscillations of 305—307
Aeroplane wing, free oscillations of 266 328—331
Aeroplane wing, semi-rigid 266 305
Aeroplane wing, stability of 266
Aeroplane wing, static twist of 325—327
Aeroplane, diagram for flutter characteristics of 359
Aeroplane, free disturbed steady motion of 284—287
Aeroplane, mass-balance of control surfaces of 302
Aeroplane, motion of 267—269
Aeroplane, stability of 285
Aeroplane, steady motion of 268
Aileron, oscillations of wing with 328—331
Airscrew blade, oscillations of beam resembling 318—320
Aitken's formulae 149 151
Aitken, A.G. 2 12 148 149 151 329
Algebraic equations of general degree, expressed as characteristic equation 148
Algebraic equations of general degree, number and situation of real roots of 152—153
Algebraic equations of general degree, numerical solution of 148—150
Algebraic equations of general degree, test functions for 164—155
Algebraic equations, linear 27 96—97 125—133
Alternate, or skew symmetric, matrix 3 33
Analytic function 213
Angular, coordinates 250 255—256 259 267
Angular, momenta 257
Angular, velocities 248 253 255
Ankylosed coordinates 333
Ankylosis, criterion for 342 367 378
Ankylosis, defined 333
Ankylosis, experimental observations of 333 397
Ankylotic motion, defined 333 335
Ankylotic motion, equations for 344—345 378
Annuhis, flow across 229—230
Annular membrane, vibrations of 230—231 243—246 320—322
Approximate reciprocal matrix, improvement of 120—121
Associative law 4 9 35
Axes, body 256 257
Axes, carried positions of moving 250
Axes, moving, in three dimensions 250—268
Axes, moving, in two dimensions 247—249
Axes, of central conic 249
Axes, of central quadric 258
Axes, principal 257—258
Bairstgw, L. 27
Baker, H.F. 6 19 20 54 216 217 218
Beams, flexural vibrations of 318—320
Beams, torsional vibrations of 314—316
Bernoulli's method of numerical solution of algebraic equations 148
Bernoulli, D. 148
Bicexey, W.G. 32
Bilinear form, defined 28
Bilinear form, differentiated 48
Bilinear form, partitioned 29—30
Binary systems with friction, graphical method for 354—357 372—380
Binnik, A.N. 25
Bocher, M. 1
Body axes 256 257
Boundary conditions, order of 189 190 191
Boundary problems 186—211 see “Two-point “Linear
Bounded oscillations 333 334
Bounds for moduli of elements, of an integrated matrix 52 55
Bounds for moduli of elements, of powers of a matrix 41 43 145—147
Brackets, special use of, for matrices 1 2
Bryant, L.W. 17
Burnside, W.S. 14
Canonical form, for lambda-matrices 91—92 181
Canonical form, for square matrices 89—90 93—96
Canonical form, of dynamical matrix 298 310
Cantilever, torsional oscillations of uniform 314—316
Carried axes 250
Carter, B.C. 318 37
Cayley — Hamilton theorem 70—73
Cayley, A. 70
Centrifugal, potential function 277
Centrifugal, stiffnesses 278 279
Change of reference axes, in three dimensions 260—256
Change of reference axes, in two dimensions 247—249
Characteristic numbers, calculated by collocation and Galerkn's method 224 226—228 230—231
Characteristic numbers, defined 187—188
Characteristic numbers, for annular membrane 230—231 243—245 320—322
Characteristic numbers, for stretched string 188
Characteristic numbers, of a square matrix 64 see
Characteristic, determinant 157
Characteristic, equation 64 67 70 157 205
Characteristic, equation, constructed by iterative method 142
Characteristic, function 64
Characteristic, function, reduced 70 72
Characteristic, matrix 64
Characteristic, matrix, adjoint and derived ad joints of 64 73—78
Characteristic, Segre 94
ChristoffeFs symbol 272
Christoffel, E.B. 272
Classical submatrices 94
Coefficients, method of mean 232—245
Cofaotors 16
Collar, A.R. 10, 11, 3S 39 43 44 45
Collineatory transformation 66 69 93 94 206
Collocation, solution of differential equations by 224—232
Column matrix 2
Columns, modal see “Modal columns”
Commutative law of addition 4
Commute, matrices which 6 see
Complementary function 157 178—182
Complete motion, defined 335
Complete motion, graphical method for discussion of 354—357 372—380
Complete motion, with one coordinate frictionally constrained 339—344
Complex scalars represented by matrices 35
Confluent, form of Sylvester's theorem 83—87 134
Confluent, special solution of differential equations 198—200
Conformability, of matrices 6 9 25
Conformability, of partitioned matrices 14
Congruent transformation 29 31
Conic, axes of 249
Conic, test 387—389
Conjugate, matrices 33
Conjugate, quaternions 36
Conservative and non-conservative forces 263—265
Conservative system, conditions for equilibrium of 264
| Conservative system, disturbed from equilibrium 281—282 291—300
Conservative system, disturbed from steady motion 282—283
Conservative system, iterative method for linear 308—310
Conservative system, modal columns for linear 199 291—295 299 300 308
Conservative system, normal or principal coordinates for linear 295—298
Conservative system, orthogonal properties of modes for linear 299 300 309.
Conservative system, Rayleigh's principle for linear 299 300 310 315
Conservative system, reciprocal theorem for 265
Conservative system, with equal frequencies 198—200 292—295 309 310 322—325
Conservative system, with ignorable coordinates 272—274 282—283
Constituent motions of linear dynamical systems, general nature of 289—291 359
Constituent solutions, numerical evaluation of 172—175
Constituent solutions, of linear differential equations 167—175
Constituent solutions, of linear dynamical equations 288
Constraint, geometric or kinematic 259—260 261 270
Constraint, one-sided 260
Constraints 270
Continuation formula for differential equations 219—222
Continued products of matrices, computed by use of subproducts 11—12
Continued products of matrices, computed from left to right or right to left 10 11 12 221
Continued products of matrices, rules for construction of 9—10
Control surfaces of aeroplanes, mass-balance of 302
Convergence, of Beries of matrices 40 81
Convergence, of matrix exponential series 42 46
Convergence, of matrizant 55 218
Coordinates, angular 250 255—266 259 267
Coordinates, ankylosed 333
Coordinates, generalised 261
Coordinates, ignorabie 272—274 282—283
Coordinates, normal or principal 295—298
Couplings 284
Crankshaft, torsional oscillations of 316—318
Critical, frequency 307
Critical, parameters, for dynamical systems 291
Critical, root of determinantal equation 359 382
Critical, speed for flutter 291 302 368 359 389
Cross, dampings 284
Cross, stiffnesses 281 284
Cross-multiplication 151 153
Cuixis, O.E. 47
Cyclic coordinates see “Ignorabie coordinates”
D-determinants, defined 157
D-determinants, of equivalent systems of differential equations 158
D-matrix 157 159
Damping, coefficients 284 339
Damping, diagram for tail oscillations 359 361
Damping, matrix 284 288 385
Dampings, direct and cross 284
Darboux, M.G. 218 22
Decaying oscillations 333 334 359 361
Degeneracy, full 67 86
Degeneracy, multiple 18 see
Degeneracy, of a square matrix 18
Degeneracy, simple 18 see
Degeneracy, Sylvester's law of 23 24
Degrees of freedom 269 261 273
Derivatives, acceleration 284
Derivatives, aerodynamical 264 285 286
Derivatives, for coupled oscillations of an aerofoil 386 386 391
Derivatives, generalised aerodynamical 284
Derivatives, of matrices 43—44
Derived adjoint matrices, for simple first-order system 206
Derived adjoint matrices, of characteristic matrix 73—77
Derived adjoint matrices, of lambda-matrix 61 62 64 166
Determinantal equation, critical roots of 369
Determinantal equation, defined 61 157
Determinantal equation, for first-order system of differential equations 205
Determinantal equation, for linear dynamical equations 288
Determinantal equation, general theorems on roots of 61 166
Determinantal equation, multiple roots of 61—64 166—181 184 198 199 206 288 292—295 296 298
Determinantal equation, nature of roots of, for linear conservative system 291—295
Determinantal equation, notation for roots of 61
Determinants, cofactors of elements of 16
Determinants, computation of 106—108 110 115 120
Determinants, differentiation of 16
Determinants, minor 16
Determinants, of square matrices 16
Determinants, symmetrical 34
Determinants, test 154 291
Determinants, whose minors of a certain order all vanish 17
Deviation, equations of 280
Diagonal, majbrix 3 12—13 23 66 89 91 93
Diagonal, order 161
Diagonal, principal 3
Diagonal, systems of linear differential equations 160
Difference equation, linear 73 148
Differential equations, linear see “Linear ordinary differential equations Linear
Differential operators, change of variables in 48—52
Differential operators, matrices of 46—51 156
Differential operators, transformation of quadratic 51—52
Differentiation, notation for 44
Differentiation, of bilinear or quadratic forms 48
Differentiation, of determinants 16
Differentiation, of matrices 43—52
Differentiation, of matrix exponential function 45—46
Direct, dampings 284
Direct, elastic stiffnesses 281
Direct, solution of linear ordinary differential equations 191—195 201 207—209 295
Direct, stifnesses 284
Direction cosines, matrix of 34 247 251
Discriminants, defined 30
Discriminants, of kinetic energy function 272
Discriminants, of quadratic form 30—33
Displacement diagram, for graphical discussion of friction problems 355—357 373—374
Distributive law 10
Disturbances, effects of arbitrary initial 334
Disturbances, effects of large initial 334 361 368
Disturbed, equilibrium of conservative system 281
Disturbed, motions 280—281
Disturbed, steady motion of aeroplane 284—287
Disturbed, steady motion of conservative system 282—283
Divergence 290
Division, of lambda-matrices 58—80
Division, of matrices 22
Division, on the left and on the right 60
Divisors, elementary 92
Dominant latent roots, calculation of 134—143
Dominant latent roots, defined 80
Down-stroke 335
Duncan, W.J. 10 11 15 24 30 40 42 44 45
Dynamical equations, for systems with solid friction 335—345
Dynamical equations, Hamilton's 274—276 289
Dynamical equations, Lagrange's 269—272 277—279
Dynamical equations, linear see “Linear dynamical equations”
Dynamical matrix, canonical form of 298 310
Dynamical matrix, constructed by use of flexibility matrix 309
Dynamical matrix, defined 308
Dynamical matrix, modal matrix of 298
Dynamical systems, conservative see “Conservative system”
Dynamical systems, constituent motions of linear 289—291
Dynamical systems, defined 268
Dynamical systems, forced oscillations of 302—307
Dynamical systems, geometrical equations of 262
Dynamical systems, holonomous 260 261 269—272
Dynamical systems, non-holonomous 260
Dynamical systems, non-linear 334
Dynamical systems, reciprocal property of 276
Dynamical systems, with ignorabie coordinates 272—274 282—283
Dynamical systems, with solid friction see “Solid friction”
Eddington, Sir A. 8
Elastic stiffnesses 264 281
Element, of matrix 1
Elementary, divisors 92
Elementary, operations on matrices 87—89 90 98 97
Energy, equation of 276
Energy, kinetic 257 270 272 275 282
Energy, potential 263 264 271 326
Equality of matrices 4
Equation, algebraic, of general degree 148—155
Equation, characteristic 64 67 70 142 157 206
|
|
|
| Ðåêëàìà |
|
|
|
|
|
|
|
|
Î ïðîåêòå