|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Frazer R.A., Duncan W.J., Collar A.R. — Elementary Matrices |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Matrix, dynamical 308 309 310
Matrix, exponential function of a square 41—43 45—46 209—211 221 222 232
Matrix, flexibility 265 309
Matrix, hermitian 33 155
Matrix, idempotent 79
Matrix, inertia 284 288
Matrix, integrated 52—56
Matrix, lambda 57 see Lambda-matrix”
Matrix, line 2
Matrix, modal 66 179 see
Matrix, multiply degenerate 18—20 .23 61 62 65 67 70 85
Matrix, non-singular 18
Matrix, null 3 23
Matrix, of a linear transformation 27
Matrix, of direction cosines 34 247 251
Matrix, of transformation, orthogonal 247 251 255
Matrix, order of 2
Matrix, orthogonal 33 34 35 247 251
Matrix, polynomial of a square 39—40 45 67 69 78—30 83—87
Matrix, powers of a square 10 37—38 67 72 73 80 133 145
Matrix, rank of a square 18 23 57 89—90 91
Matrix, rectangular 1
Matrix, resolvent of a square 78
Matrix, row 2
Matrix, scalar 13
Matrix, simply degenerate 18 61 65 71 86
Matrix, singular 18
Matrix, skew 3
Matrix, skew symmetric 3 26 33
Matrix, square 3
Matrix, stiflhess 264 284 288 308
Matrix, Sylvester's expansion for a square 86
Matrix, symmetrical 3 26 33—34 77
Matrix, total stiffness 284
Matrix, transposed 3 25
Matrix, triangular 97—106
Matrix, unit 3 13 35
Matrizant 53—56 218—219 222 232
Mean coefficients, method of 232—245
Membrane, vibrating annular 230—231 243—245 320—322
Minor determinants 16
Mittag — Leffier star 52
Mittag — Leffler, G. 52
Modal coefficient 179
Modal columns, calculated by iterative methods 141—145 150 351 308—310
Modal columns, connected with the characteristic matrix 64—69
Modal columns, defined 64 179
Modal columns, for general linear dynamical system 288—290 327 329 330
Modal columns, for linear conservative system 199 291—295 299 300 308—310 312—314 324 325
Modal columns, for simple first-order system 206
Modal columns, for systems with solid friction 336
Modal columns, orthogonal properties of, for conservative systems 299 300
Modal columns, properties of 77
Modal columns, relations between, for dissipative systems 301
Modal matrix, defined 66 179
Modal matrix, for Bystems with solid friction 336
Modal matrix, for linear dynamical system 289
Modal matrix, for simple first-order system 206
Modal matrix, of dynamical matrix 298
Modal matrix, of polynomial of a matrix 69
Modal matrix, of symmetrical matrix 77 259 265
Modal matrix, reciprocal of 77 86
Modal row 336
Moments of inertia, generalised 281 284
Moments of inertia, principal 257—258
Momentum, angular 257
Momentum, generalised 274—276
Morris, J. 132 133 9
Morris, method of, for solution of linear algebraic equations 132
Moving axes, angular momenta referred to 257
Moving axes, angular velocities of 248 253 255
Moving axes, carried positions of 250
Moving axes, defined 246
Moving axes, in three dimensions 250—256
Moving axes, in two dimensions 247—249
Moving axes, kinetic energy expressed for 257
Moving axes, Lagrange'B equations referred to 277—279
Moving axes, velocities and accelerations referred to 248 256
Multi-cylinder engine, torsional oscillations of 316—318
Multiplication, of lambda-matrioes 58
Multiplication, of matrices, rules for 6
Multiplication, of partitioned matrioes 14
Multiply degenerate matrioes, adjointe of 21 62 63 66 123 125 173 174
Multiply degenerate matrioes, corresponding to multiple latent roots 65 67 69 70 71 85 87
Multiply degenerate matrioes, corresponding to multiple roots of determinantal equation 61 63
Multiply degenerate matrioes, defined 18
Multiply degenerate matrioes, expressed as products 20
Multiply degenerate matrioes, products of 23
Muzr, Sir T. 48 49 50
National Physical Laboratory, experiments at the 332 333 382 395—398
Non-holonomous systems 260
Normal coordinates 295—298
Null, matrices 3
Null, product, square matrices with 23—24
Nullity, denned 18
Nullity, Sylvester's law of 23
One-point boundary problem, confluent special solution for standard 198—200
One-point boundary problem, defined 186
One-point boundary problem, direct solution of 191—195 207—209 295
One-point boundary problem, notation for 188—189
One-point boundary problem, order of conditions for 189 190—191
One-point boundary problem, power series solution of 209—211
One-point boundary problem, speoial solution for standard 195—197 203—205 207
One-point boundary problem, standard 189—190
One-sided constraint 260
One-signed quadratic forms 30
Operational formulae connected with partial fractions 177—178 184 190 196 203 204
Operators, matrices of differential 46—51 156
Operators, selective 82
Order, of matrix 2
Order, of one-point boundary conditions 189 190—191
Order, of system of linear differential equations 156
Ordinary differential equations, linear see “Linear ordinary differential equations”
ordinary points of linear differential equations 212
Orthogonal, Matrix 33 34 35 247 251
Orthogonal, property 77 259 299 300
Oscillations, bounded 333 334
Oscillations, decaying 333 334 359 361
Oscillations, flexural, of tapered beam 318—320
Oscillations, forced, of aerodynamical systems 302—307
Oscillations, of aeroplane tail see “Aeroplane tail”
Oscillations, of aeroplane wing 266 305—307 328—331
Oscillations, of beams 309 314—316 318—320
Oscillations, of systems with solid friction see “Solid friction”
Oscillations, of triple pendulum 310—314
Oscillations, pitching, of an aerofoil 382—398
Oscillations, resonant forced 183 305
Oscillations, spasmodic 332 333
Oscillations, steady see “Steady oscillations”
Oscillations, torsional, of multi-cylinder engine 316—318
Oscillations, torsional, of uniform cantilever 314—316
Oscillations, transverse, of annular membrane 230—231 243—245 320—322
Oscillations, transverse, of stretched string 188
Oscillations, unbounded 333 334 see
Oscillatory instability, conditions for 291
Overtones, calculation of, by iterative methods 309 312—314 325 330—331
Panton, A.W. 14
Parameters, critical 291
Partial, differential equations, linear 50—51 227
Partial, differential operators, matrices of 47—51
Partial, fractions, matrix formulae dependent on 78 83 175—178 184 190 196 203 204
Particular integral 157 183—185 196 209
Partitioning, of bilinear and quadratic forms 29—30 272
Partitioning, of matrices 13—15
Peano — Baker method of integration 216 217—218
Peano, G. 216 217 218
Pendulum, oscillations of a triple 310—314
Permutable matrices 6 7 42 44
Piaggio, H.T.H. 28
Pitching oscillations of an aerofoil, conditions for steady friotional 387—394
| Pitching oscillations of an aerofoil, derivatives appropriate to 385—386 391
Pitching oscillations of an aerofoil, design of apparatus for 384—394
Pitching oscillations of an aerofoil, experiments on 382—384 395—398
Planck, M. 28
Poinoare, H. 333
Point, or cohimn matrix 2
Polynomial of a square matrix, constructed by coDineatory transformation 67
Polynomial of a square matrix, defined 39
Polynomial of a square matrix, evaluated by Sylvester's theorem 78—80 83—37
Polynomial of a square matrix, factorisation of 39 40
Polynomial of a square matrix, latent roots and modal matrix of 69
Polynomial of a square matrix, reduction of, by Cayiey — Hamilton theorem 72
Polynomial of a square matrix, Taylor's theorem for 44—45
Positional coordinates, of a rigid body 259 see “Generalised
Positive definite quadratic form 30
Postdivision 22
Postmultiplioation 6
potential energy 263 264 271 326
Potential, centrifugal 277
Potential, kinetic 271
Powers of a square matrix, constructed by oollineatory transformation 67
Powers of a square matrix, denned 10 37
Powers of a square matrix, fractional 38 81 82
Powers of a square matrix, high 80 133—146
Powers of a square matrix, linear difference equation satisfied by 73 148
Powers of a square matrix, reduction of, by Cayley — Hamilton theorem 72
Powers of a square matrix, upper bounds for moduli of elements in 41 43 125—147
Predivision 22
Premultiplication 6
Prime, or row matrix 2
Principal, axes 257—268
Principal, coordinates 296—298
Principal, diagonal 3
Principal, directions of loading 265—266
Product chain, or continued product, of matrices 9—12 221
Products of inertia, elimination of, by conversion to principal axes 257
Products of inertia, generalised 281 284
Products of matrices, abbreviated rules for 8
Products of matrices, continued 9—12 221
Products of matrices, denned 6
Pure strain 259
Quadratic differential operators 49—52
Quadratic form, defined 28
Quadratic form, differentiation of 48
Quadratic form, discriminants of 30—33 272
Quadratic form, one-signed 30
Quadratic form, partitioned 29—30 272
Quadratic form, positive definite 30
Quadrio, axes of a central 258
Quaternions, represented by matrices 35—36
Rank, of a lambda-matrix 57 91 182
Rank, of a square matrix 18 23 89—90
Rank, of equivalent matrices 89—90
Rayleigf, Lord 299 300 310 315
Rayleigh's principle, for conservativesystems 299—300 310 315
Rayleigh's principle, generalised for special dissipative systems 300—301
Reciprocal, improvement of an approximate 120—121
Reciprocal, of lambda-matrix 53
Reciprocal, of matrix 22
Reciprocal, of modal matrix 77 86
Reciprocal, of skew symmetric matrix 26
Reciprocal, of symmetrical matrix 26
Reciprocal, of triangular matrix 103—106
Reciprocal, property of a dynamical system 276
Reciprocal, theorem for conservative systems 265
Reciprocation, by direct operation on rows 119—120
Reciprocation, by method of postmultipliers 109—112
Reciprocation, by method of submatrices 112—118
Reciprocation, reversal rule for 25
Rectangular matrix 1
Reduced characteristic function 70 72
Reducing variables, defined 195
Reducing variables, displacements, velocities, and accelerations expressed in terms of 336 337 340 379
Reducing variables, for system with solid friction 336 337
Reducing variables, recurrence relations for 341 342
Reference axes see “Axes Frame
Regular singularity 215
Remainder theorems for lambda-matrices 59 60 70
Resolvent, of a square matrix 78
Resonance 183 305
Reversal of order in products 25
Rodrigues' formula 254
Rodrigues, O. 254
Roots, latent 64—87 see
Roots, of algebraic equations see “Algebraic equations of general degree” “Linear
Roots, of determinants! equation see “Determinantal equation”
Roots, of matrices 38 81 82
Rotations, convention regarding sign of 247
Rotations, matrices representing finite 248—249 251—254
Routh's test functions for stability 154
Routh, E.J. 151 154 197 13
Row matrix 2
Rowelx, H.S. 41
Rudder-fuselage flutter see “Tail flutter”
Scalar, equations, expressed as matrix equation 5
Scalar, matrix 13
Scalar, multipliers 4 5
Scruton, C. 40
Segre characteristic 94
Segre, C. 94
Selective operators 82
Semi-period oquation, for steady frictional oscillations 346 348—360 364 370 393
Semi-rigid body 266
Semi-rigid cantilever 266
Semi-rigid wing 266 305
Sezawa, K. 35
Simple first-order system of differential equations, adjoint matrices for 205
Simple first-order system of differential equations, continuation formula for 220—222
Simple first-order system of differential equations, defined 202 216
Simple first-order system of differential equations, determinantal equation for 205
Simple first-order system of differential equations, direct solution of 207 208
Simple first-order system of differential equations, general solution of 206
Simple first-order system of differential equations, modal columns for 206
Simple first-order system of differential equations, power series solution of 209—211
Simple first-order system of differential equations, special solution of 207
Simply degenerate matrices, adjoints of 21 61 62 63 65 68 76 123 124
Simply degenerate matrices, corresponding to simple or multiple latent roots 65 66 68 71 86
Simply degenerate matrices, corresponding to simple or multiple roots of determinantal equation 61 62 63
Simply degenerate matrices, defined 18
Singular matrices see also “Multiply degenerate matrices” “Simply
Singular matrices, defined 18
Singular matrices, expressed as products 20
Singularities, of linear differential equations 212—215 221
Skan, S.W. 23
Skew, matrix 3
Skew, symmetric matrix 3 26 33
Slug, definition of 387
Small motions, construction of equations of 280—281
Small motions, of aerodynamical systems 283—284
Smith's canonical form for lambda-matrices 91—92 181
Smith's transformation, for an operational row 50
Smith, H.J.S. 91 92 131
Smith, T. 4 50
Solid friction, dynamical equations for systems with 335—345
Solid friction, graphical method for systems with 354—357 372—380
Solid friction, influence of, on critical speed for flutter 362
Solid friction, influence of, on oscillations of systems 332 333
Solid friction, measurements of 395
Solid friction, oscillations of aeroplane tails with 359—381
Solid friction, pitching oscillations of an aerofoil constrained by 382—398
Solid friction, static and dynamic 332
Solid friction, steady oscillations of systems with, ate Steady oscillations system with single degree of freedom and 342—344
Sories of matrices, infinite 40—41 53 81
Spasmodic oscillations 332 333
Special solution, confluent form of 198—200
Special solution, for general first-order system 203—205
Special solution, for simple first-order system 207
Special solution, for standard one-point boundary problems 195—197
Spectral set, of operators 82
Sphere, rolling on a fixed plane 260
|
|
|
| Ðåêëàìà |
|
|
|
|
|
|
|
|
Î ïðîåêòå