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| Frazer R.A., Duncan W.J., Collar A.R. — Elementary Matrices |
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| Предметный указатель |
Spiral diagrams, for graphical discussion of friction problems 356—357 374
Square matrix, definition of 3
Stability, of an aeroplane 285
Stability, of an aeroplane wing 266
Stability, of equilibrium of a conservative system 264
Stability, of steadv frictional oscillations 350—353 360—361 362 382
Stability, test functions and determinants for 154—155 291 388 389
Standard one-point boundary problem, defined 189
Standard one-point boundary problem, special solution for 195—200 203—206 207
Starting instant 335
Steady motion, aeroplane disturbed from 284—287
Steady motion, conservative system with ignorable coordinates disturbed from 282—283
Steady motion, disturbance from 280
Steady motion, of an aeroplane 268
Steady oscillations, conditions for, when only one coordinate is frictionally constrained 345—350
Steady oscillations, graphical treatment of conditions for 387—389
Steady oscillations, of aerofoil with solid friction 382 387—397
Steady oscillations, of aeroplane tails with solid friction 360—372 375
Steady oscillations, semi-period equation for 346 348—350 364 370 393
Steady oscillations, stability of 350—353 360 361 362 382
Steady oscillations, treatment of conditions for, based on inertias 389—392
Stiffness, aerodynamical 264 284 385
Stiffness, centrifugal 278 279
Stiffness, coefficient 264 338
Stiffness, cross 284
Stiffness, direct 284
Stiffness, direct elastic 281
Stiffness, elastic 264
Stiffness, elastic cross 281
Stiffness, line 388 389
Stiffness, matrix 264 284 288 308
Stiffness, point 388
Stopping instant 335
Strain, homogeneous 258
Strain, pure 259
String, oscillations of a stretched 188
Structural problems, linear algebraic equations in 132
Sturm's functions 152—153
Sturm, J.C.F. 96 152 153
Subdominant latent roots, calculation of 143—144 151
Submatrices, bilinear and quadratic forms expressed by 29—30 272
Submatrices, defined 13—15
Submatrices, of simple classical type 94
Submatrices, reciprocation by method of 112—118
Subproduets, use of, in calculation of continued products 11
Subsidence 290
Substitution, linear 26—27 64
Summation, of infinite series of matrices 41 81
Summation, of matrices 4
Superdiagonal elements 93
Sylvester's expansion, coefficients in, calculated by iterative methods 138—141 310
Sylvester's expansion, confluent form of 83—87 134
Sylvester's expansion, constructed 78—79
Sylvester's expansion, dominant latent roots calculated by 80 133—138
Sylvester's expansion, fractional powers of a matrix obtained by 81
Sylvester's expansion, infinite series of matrices summed by 81
Sylvester's expansion, properties of coefficients in 79 82
Sylvester's law of degeneracy 23 24
Sylvester, J.J. 23 24 78
Symmetrical matrix, adjoint of 34
Symmetrical matrix, defined 3
Symmetrical matrix, latent roots of 155
Symmetrical matrix, modal matrix of 77 259 265
Symmetrical matrix, reciprocal of 26
Symmetrical, determinants 34
| Symmetrical, matrices, products of 26 33
Tail flutter, critical speed for 359 363
Tail flutter, damping and frequency diagrams relating to 359 361
Tail flutter, influence of solid friction on 360 362
Tail flutter, wind tunnel experiments on 332 333 361
Tail oscillations, friction theory applied to 359—381
Tail oscillations, steady 360—372 375 376 380
Tait, P.G. 3
Taylor's theorem for matrices 44—45
Temple, G. 32
Tensor 36
Terminal, equations 342
Terminal, instant 335
Test, conic 387—389
Test, determinants and functions for stability 154—155. 291 388 389
Torsional oscillations, of aeroplane fuselage see “Tail oscillations”
Torsional oscillations, of multi-cylinder engine 318—318
Torsional oscillations, of uniform cantilever 314—316
Total stiffness matrix 284
Transformation, collineatory 66 69 93 94 206
Transformation, Congruent 29 31
Transformation, linear 26—27 64
Transformation, matrix of a linear 27
Transformation, of generalised coordinates 282
Transformation, orthogonal matrix of 247 251
Transformation, Smith's, for an operational row 50
Transposition of matrices 3 25
Transverse oscillations, of a stretched string 188
Transverse oscillations, of an annular membrane 230—231 243—245 320—322
Triangular matrix, denned 97
Triangular matrix, reciprocal of 103—106
Triangular matrix, reduced to diagonal iSrm 102—103
Triangular matrix, reduction of non-singular matrix to 97—102
Triangular systems, of linear ordinary differential equations 160—162
Triple pendulum, oscillations of 310—314
Turnbxjll, H.W. 2 46
Twist of an aeroplane wing, static 325—327
Two-point boundary problem, defined 186
Two-point boundary problem, direct solution of 201
Two-point boundary problem, notation for 200—201
Two-point boundary problem, power series solution of 211
Unbounded oscillations 333 334
Unit matrix 3 13 35
Up-stroke 335
Upper bounds, for an integrated matrix 52 55
Upper bounds, for powers of a matrix 41 43 145—147
Vector function, linear 258
Vector, components of, referred to moving axes 247—248 251 256
Vector, of first kind, or row matrix 2
Vector, of second kind, or column matrix 2
Vibrations see “Oscillations”
Virtual work 262—264 270 277
von Scrleppe, B. 34
Wedderburn, J.H.M. 7
Whittaker, E.T. 31
Williams, D.H. 17
Wind tunnel experiments, on pitching oscillations of aerofoil 382 396—398
Wind tunnel experiments, on tail flutter 332 333 361
Wing, critical speed for flatter of 302 307
Wing, forced oeofflaticms of 305—307
Wing, free oscillations of 206 328—331
Wing, semi-rigid 266 305
Wing, stability of 266
Wing, static twist of 326—327
Work, virtual 262—264 270 277
Yaw, angular displacements in 268 332 333
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