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Frazer R.A., Duncan W.J., Collar A.R. Ч Elementary Matrices
Frazer R.A., Duncan W.J., Collar A.R. Ч Elementary Matrices

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Ќазвание: Elementary Matrices

јвторы: Frazer R.A., Duncan W.J., Collar A.R.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1952

 оличество страниц: 416

ƒобавлена в каталог: 11.04.2008

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ѕредметный указатель
Abbreviated rules for matrix products      8
Absent coordinates      see УIgnorable coordinatesФ
Absolute velocity and acceleration      246
Acceleration derivatives      284
Addition and subtraction of matrices      4
Adjoint matrix, defined      21
Adjoint matrix, derived      see УDerived adjoint matricesФ
Adjoint matrix, for simple first-order system      205
Adjoint matrix, of characteristic matrix      65 70 73Ч78
Adjoint matrix, of lambda-matrix      61Ч64 165Ч167
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 121Ч125 172Ч175
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      302Ч307
Aerodynamical systems, small motions of      283Ч284
Aerofoil, frictional pitching oscillations of      382Ч397
Aerofoil, non-frictional pitching oscillations of      397 398
Aeroplane tail, ankylotic motion of      378Ч379
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      360Ч372 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      305Ч307
Aeroplane wing, free oscillations of      266 328Ч331
Aeroplane wing, semi-rigid      266 305
Aeroplane wing, stability of      266
Aeroplane wing, static twist of      325Ч327
Aeroplane, diagram for flutter characteristics of      359
Aeroplane, free disturbed steady motion of      284Ч287
Aeroplane, mass-balance of control surfaces of      302
Aeroplane, motion of      267Ч269
Aeroplane, stability of      285
Aeroplane, steady motion of      268
Aileron, oscillations of wing with      328Ч331
Airscrew blade, oscillations of beam resembling      318Ч320
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      152Ч153
Algebraic equations of general degree, numerical solution of      148Ч150
Algebraic equations of general degree, test functions for      164Ч155
Algebraic equations, linear      27 96Ч97 125Ч133
Alternate, or skew symmetric, matrix      3 33
Analytic function      213
Angular, coordinates      250 255Ч256 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      344Ч345 378
Annuhis, flow across      229Ч230
Annular membrane, vibrations of      230Ч231 243Ч246 320Ч322
Approximate reciprocal matrix, improvement of      120Ч121
Associative law      4 9 35
Axes, body      256 257
Axes, carried positions of moving      250
Axes, moving, in three dimensions      250Ч268
Axes, moving, in two dimensions      247Ч249
Axes, of central conic      249
Axes, of central quadric      258
Axes, principal      257Ч258
Bairstgw, L.      27
Baker, H.F.      6 19 20 54 216 217 218
Beams, flexural vibrations of      318Ч320
Beams, torsional vibrations of      314Ч316
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      29Ч30
Binary systems with friction, graphical method for      354Ч357 372Ч380
Binnik, A.N.      25
Bocher, M.      1
Body axes      256 257
Boundary conditions, order of      189 190 191
Boundary problems      186Ч211 see УTwo-point УLinear
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 145Ч147
Brackets, special use of, for matrices      1 2
Bryant, L.W.      17
Burnside, W.S.      14
Canonical form, for lambda-matrices      91Ч92 181
Canonical form, for square matrices      89Ч90 93Ч96
Canonical form, of dynamical matrix      298 310
Cantilever, torsional oscillations of uniform      314Ч316
Carried axes      250
Carter, B.C.      318 37
Cayley Ч Hamilton theorem      70Ч73
Cayley, A.      70
Centrifugal, potential function      277
Centrifugal, stiffnesses      278 279
Change of reference axes, in three dimensions      260Ч256
Change of reference axes, in two dimensions      247Ч249
Characteristic numbers, calculated by collocation and Galerkn's method      224 226Ч228 230Ч231
Characteristic numbers, defined      187Ч188
Characteristic numbers, for annular membrane      230Ч231 243Ч245 320Ч322
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 73Ч78
Characteristic, Segre      94
ChristoffeFs symbol      272
Christoffel, E.B.      272
Classical submatrices      94
Coefficients, method of mean      232Ч245
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      224Ч232
Column matrix      2
Columns, modal      see УModal columnsФ
Commutative law of addition      4
Commute, matrices which      6 see
Complementary function      157 178Ч182
Complete motion, defined      335
Complete motion, graphical method for discussion of      354Ч357 372Ч380
Complete motion, with one coordinate frictionally constrained      339Ч344
Complex scalars represented by matrices      35
Confluent, form of Sylvester's theorem      83Ч87 134
Confluent, special solution of differential equations      198Ч200
Conformability, of matrices      6 9 25
Conformability, of partitioned matrices      14
Congruent transformation      29 31
Conic, axes of      249
Conic, test      387Ч389
Conjugate, matrices      33
Conjugate, quaternions      36
Conservative and non-conservative forces      263Ч265
Conservative system, conditions for equilibrium of      264
Conservative system, disturbed from equilibrium      281Ч282 291Ч300
Conservative system, disturbed from steady motion      282Ч283
Conservative system, iterative method for linear      308Ч310
Conservative system, modal columns for linear      199 291Ч295 299 300 308
Conservative system, normal or principal coordinates for linear      295Ч298
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      198Ч200 292Ч295 309 310 322Ч325
Conservative system, with ignorable coordinates      272Ч274 282Ч283
Constituent motions of linear dynamical systems, general nature of      289Ч291 359
Constituent solutions, numerical evaluation of      172Ч175
Constituent solutions, of linear differential equations      167Ч175
Constituent solutions, of linear dynamical equations      288
Constraint, geometric or kinematic      259Ч260 261 270
Constraint, one-sided      260
Constraints      270
Continuation formula for differential equations      219Ч222
Continued products of matrices, computed by use of subproducts      11Ч12
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      9Ч10
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 255Ч266 259 267
Coordinates, ankylosed      333
Coordinates, generalised      261
Coordinates, ignorabie      272Ч274 282Ч283
Coordinates, normal or principal      295Ч298
Couplings      284
Crankshaft, torsional oscillations of      316Ч318
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 УIgnorabie coordinatesФ
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      43Ч44
Derived adjoint matrices, for simple first-order system      206
Derived adjoint matrices, of characteristic matrix      73Ч77
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      61Ч64 166Ч181 184 198 199 206 288 292Ч295 296 298
Determinantal equation, nature of roots of, for linear conservative system      291Ч295
Determinantal equation, notation for roots of      61
Determinants, cofactors of elements of      16
Determinants, computation of      106Ч108 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 12Ч13 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 УLinear ordinary differential equations Linear
Differential operators, change of variables in      48Ч52
Differential operators, matrices of      46Ч51 156
Differential operators, transformation of quadratic      51Ч52
Differentiation, notation for      44
Differentiation, of bilinear or quadratic forms      48
Differentiation, of determinants      16
Differentiation, of matrices      43Ч52
Differentiation, of matrix exponential function      45Ч46
Direct, dampings      284
Direct, elastic stiffnesses      281
Direct, solution of linear ordinary differential equations      191Ч195 201 207Ч209 295
Direct, stifnesses      284
Direction cosines, matrix of      34 247 251
Discriminants, defined      30
Discriminants, of kinetic energy function      272
Discriminants, of quadratic form      30Ч33
Displacement diagram, for graphical discussion of friction problems      355Ч357 373Ч374
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      280Ч281
Disturbed, steady motion of aeroplane      284Ч287
Disturbed, steady motion of conservative system      282Ч283
Divergence      290
Division, of lambda-matrices      58Ч80
Division, of matrices      22
Division, on the left and on the right      60
Divisors, elementary      92
Dominant latent roots, calculation of      134Ч143
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      335Ч345
Dynamical equations, Hamilton's      274Ч276 289
Dynamical equations, Lagrange's      269Ч272 277Ч279
Dynamical equations, linear      see УLinear dynamical equationsФ
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 УConservative systemФ
Dynamical systems, constituent motions of linear      289Ч291
Dynamical systems, defined      268
Dynamical systems, forced oscillations of      302Ч307
Dynamical systems, geometrical equations of      262
Dynamical systems, holonomous      260 261 269Ч272
Dynamical systems, non-holonomous      260
Dynamical systems, non-linear      334
Dynamical systems, reciprocal property of      276
Dynamical systems, with ignorabie coordinates      272Ч274 282Ч283
Dynamical systems, with solid friction      see УSolid frictionФ
Eddington, Sir A.      8
Elastic stiffnesses      264 281
Element, of matrix      1
Elementary, divisors      92
Elementary, operations on matrices      87Ч89 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      148Ч155
Equation, characteristic      64 67 70 142 157 206
1 2 3 4
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