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



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Íàçâàíèå: Elementary Matrices

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

ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1952

Êîëè÷åñòâî ñòðàíèö: 416

Äîáàâëåíà â êàòàëîã: 11.04.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Equation, detei-minantal      see “Determinantal equation”
Equation, indicial      215
Equation, semi-period, for steadv frictional oscillations      346 348—350 364 370 393
Equations, dynamical, for frictional systems      335—345
Equations, geometrical, of a dynamical system      262 277
Equations, Hamilton's dynamical      274—276 289
Equations, Lagrange's dynamical      164 194 195 197 269—272 277—279 289
Equations, linear algebraic      27 98—97 125—133
Equations, linear difference      73 148
Equations, linear dyoamical      see “Linear dynamical equations”
Equations, linear ordinary differential      see “Linear ordinary differential equations”
Equations, linear partial differential      60—52 227
Equations, terminal      342
Equilibrium, conditions for      262—265
Equilibrium, conservative system disturbed from      281
Equivalent, latabda-matrices      90—92
Equivalent, matrices      89
Equivalent, systems of differential equations      158 159 161
Euler, L.      250
Existence theorems      212—214
Exponential function of square matrix, applied in method of mean coefficients      232
Exponential function of square matrix, defined      41—43
Exponential function of square matrix, differentiation of      45—46
Exponential function of square matrix, solution of differential equations by      209—211 221 333
Factors, invariant      91—92
Factors, linear      92
Fields of force, conservative and non-conservative      263—265
Finite rotations, matrices representing      118—249 251—254
Flexibilities      265
Flexibility matrix, defined      265
Flexibility matrix, used to calculate dynamical matrix      309
Flexural oscillations of tapered beam      318—320
Flexure-torsion oscillations of aeroplane wing      266 30£~307.
Fluid flow across annulus      229—230
Flutter, critical speed for      291 302 307 358 359 389
Flutter, experimental observations of      332 333 395
Flutter, influence of solid friction on      360 362
Flutter, practical meaning of      359
Flutter, simple theory of      358
Forced motion of deviation      280
Forced oscillations, of aerodynamical systems      802—307
Forced oscillations, resonant      183 305
Forces, conservative      263—265
Forces, generalised      263—265 270 277
Forms, bilinear and quadratic      28—30
Fractional powers of matrices      38 81 82
Frame of reference, angular coordinates of a three-dimensional      250 255 256
Frame of reference, angular momenta referred to a moving      257
Frame of reference, angular velocities of a moving      248 253 255
Frame of reference, defined      246
Frame of reference, kinetic energy referred to a moving      267
Frame of reference, Lagrange's equations with a moving      277—279
Frame of reference, moving, in two dimensions      247—248
Frame of reference, velocities and accelerations referred to a moving      248 256
Frazer, R.A. 15, 21, 23, SO      36 88 39 40 42
Free, disturbed steady motion of an aeroplane      284—287
Free, motion of deviation      280
Freedom, degrees of      259 261 273
Frequencies, calculated by iterative methods      308—331
Frequencies, calculated by Rayleigh's principle      300 310 316
Frequencies, conservative system with equal      198—200 292—295 309 310 322—325
Frequency, diagram, for tail oscillations      359 361
Frequency, parameter, for aerofoil oscillations      385
Friction, solid      see “Solid friction”
Frobenius, F.G.      215
Frobenius, method of      216
Fundamental solutions of linear differential equations      214—215 219 220 223 224
Fuselage, oscillations involving torsion of      359—381
Galerkin, method of      224—231
Galerkin, V.G.      224 226 227 228 229 230 231
Generalised, aerodynamical derivatives      284
Generalised, coordinates, transformation of      282
Generalised, coordinates, velocities, and accelerations      260—262
Generalised, forces      263—265 270 277
Generalised, momenta      274—276
Generalised, moments and products of inertia      281 284
Geometric constraints      259—260 261 270
Geometrical equations, for a dynamical system      262 277
Graphical treatment, of binary frictional systems      354—367 372—380
Graphical treatment, of conditions for steady oscillations      387—389
Grossman, E.P.      26
Gyrostatic coefficients      278 279 283
Hamilton, Sir W.R.      70 274 275
Hamiltonian, equations of motion      274—276 289
Hamiltonian, function      275
Heaviside, identity of, expressed by matrices      176
Heaviside, method of      197 203—204
Heaviside, O.      176 197 202 203
Hermitian matrix      33 155
Hertz, H.      260
High powers of a matrix      80 133—145
Holonomous, or holonomic, systems, defined      260
Holonomous, or holonomic, systems, generalised coordinates of      261
Holonomous, or holonomic, systems, Hamilton's equations for      274—276
Holonomous, or holonomic, systems, Lagrange's equations for      269—272 277—279
Homogeneous, strain      258
Homogeneous, system of differential equations      157
Hooke, R.      266
Idempotent matrices      79
Ignorable coordinates, denned      272
Ignorable coordinates, disturbed steady motion of systems with      282—283
Ignorable coordinates, dynamical equations for systems with      272—274
Independent variables, change of      48—51
Index law for matrices      37—38
Indicial equation      215
Inertia, force      269
Inertia, generalised moments and products of      281 284
Inertia, matrix      284 288
Inertia, principal axes of      257—258
Infinite series of matrices      40—41 53 81
Influence numbers      265
Inge, E. L.      5
Integration of matrices      52—56
Interpolation formula, Lagrange's      40
Invariant factors      91—92
Inverse matrices      see “Reciprocal Reciprocation”
Irregular singularity      215
Isolation, method of      197
Iterative methods, for coefficients in Sylvester's expansion      138—141
Iterative methods, for construction of characteristic equation      142
Iterative methods, for frequencies      308—331
Iterative methods, for latent roots      134—138 140—145 148—151
Iterative methods, for linear algebraic equations      132—133
Iterative methods, for linear dynamical problems      308—331
Iterative methods, general remarks on      150—151 309—310
Iterative methods, modal columns calculated by      141—145 * 151 308—310
Iterative methods, overtones calculated by      309 312—314 325 330r>331
Iterative methods, twist of aeroplane wing calculated by      325—327
Jacobians, relations between      49
Jeans, Sir J.H.      333
Jeffreys, H.      16
Jones, W.P.      23 36
Kelt, and, P.      3
Kinematic constraints      259—260 261 270
Kinetic energy, discriminants of      272 337 370
Kinetic energy, expressed by generalised coordinates and velocities      270 282
Kinetic energy, expressed by generalised momenta and velocities      275
Kinetic energy, expressed by submatrices      272 282
Kinetic energy, expressed for moving axes      257
Kinetic potential      271
Kinosthenic coordinates      see “Ignorable coordinates”
Kubo, S.      35
Kussner, H.G.      33
Lagrange's equations, constructed      269—271
Lagrange's equations, expanded form of      271—272 281
Lagrange's equations, for systems referred to moving axes      277—279
Lagrange's equations, linear, direct solution of      194 195
Lagrange's equations, linear, expressed as first-order system      164 289 327
Lagrange's equations, linear, special solution of      197 198—200
Lagrange's equations, modified for ignorable coordinates      272—274 282—283
Lagrange's interpolation formula      40
Lagrange, J.L.      40 269
Lagrangian function, defined      271
Lagrangian function, modified, for ignorable coordinates      272—274 282
Lamb, Sir H.      29
Lambda-determinant      157
Lambda-matrices, equivalent      90—92
Lambda-matrices, multiplication and division of      58—60
Lambda-matrices, Smith's canonical form for      91—92 181
Lambda-matrix, adjoint of      61—64 166—167
Lambda-matrix, defined      57 157
Lambda-matrix, degree of      67
Lambda-matrix, derived adjoints of      61 62 64 166
Lambda-matrix, determinantal equation of      61 see
Lambda-matrix, elementary divisors of      92
Lambda-matrix, invariant factors of      91—92
Lambda-matrix, leading matrix coefficient of      57
Lambda-matrix, linear factors of      92
Lambda-matrix, rank of      57 91 182
Lambda-matrix, reciprocal of      58
Lambda-matrix, remainder theorems for      59 60 70
Laplacian operator, transformation: of      51
Latent roots, calculated by iterative methods      134—138 140—145 148—151
Latent roots, classical submatrices containing      94
Latent roots, defined      64
Latent roots, diagonal matrix of      66
Latent roots, dominant      80 134—143 148 309
Latent roots, equal      65 67—71 75—77 83—87 93 135 137 138 140
Latent roots, non-dominant      143—145 331 see
Latent roots, of Hermitian matrix      155
Latent roots, of matrices connected by collineatory transformation      69
Latent roots, of polynomial of a square matrix      69
Latent roots, of symmetrical matrix      155
Latent roots, situation of      155
Leading matrix coefficient, of a lambdamatrix      57
Line matrix      2
Linear algebraic equations, expressed as matrix equation      8 18
Linear algebraic equations, solution of      27 96—97 125—133
Linear algebraic equations, solution of, by direct operation on rows      130—131
Linear algebraic equations, solution of, by iterative methods      132—133
Linear algebraic equations, solution of, by post-multiplication      126—130
Linear difference equation      73 148
Linear differential equations      see “Linear ordinary differential equations” “Linear
Linear dynamical equations, confluent special solution of      198—200
Linear dynamical equations, direct solution of      191—192 194 195 295
Linear dynamical equations, for conservative system disturbed from equilibrium      281—282 291—300 308
Linear dynamical equations, for conservative system disturbed from steady motion      282—283
Linear dynamical equations, iterative solutions of      308—331
Linear dynamical equations, notation and terminology for      288—289
Linear dynamical equations, reduced to first-order Bystem      164 289 327
Linear dynamical equations, reducing variables for      195
Linear dynamical equations, special solution of      197
Linear dynamical equations, transformation of coordinates in      282
Linear factors      92
Linear ordinary differential equations with constant coefficients, "diagonal" systems of      160
Linear ordinary differential equations with constant coefficients, adjoint matrices for first-order system of      205
Linear ordinary differential equations with constant coefficients, boundary problems with      186
Linear ordinary differential equations with constant coefficients, change of order of boundary conditions for      190—191
Linear ordinary differential equations with constant coefficients, characteristic numbers for      187—188
Linear ordinary differential equations with constant coefficients, complementary function of      157 178—182
Linear ordinary differential equations with constant coefficients, confluent special solution of      198—200
Linear ordinary differential equations with constant coefficients, constituent solutions of      167—175
Linear ordinary differential equations with constant coefficients, conversion of, to first-order system      162—165 202
Linear ordinary differential equations with constant coefficients, direct solution of, for one-point boundary problem      191—195 207—209 295
Linear ordinary differential equations with constant coefficients, direct solution of, for two-point boundary problem      201
Linear ordinary differential equations with constant coefficients, equivalent systems of      158 159 181
Linear ordinary differential equations with constant coefficients, fundamental theorem for systems of      161
Linear ordinary differential equations with constant coefficients, general solution of simple first-order system of      206—207
Linear ordinary differential equations with constant coefficients, Heaviside's method for      203—204
Linear ordinary differential equations with constant coefficients, homogeneous and non-homogeneous systems of      157
Linear ordinary differential equations with constant coefficients, method of isolation for      197
Linear ordinary differential equations with constant coefficients, notation for one-point boundary problems with      188—189
Linear ordinary differential equations with constant coefficients, notation for systems of      156—157 178—180
Linear ordinary differential equations with constant coefficients, notation for two-point boundary problems with      200—201
Linear ordinary differential equations with constant coefficients, order of      156
Linear ordinary differential equations with constant coefficients, particular integral of      157 183—185 1G8 209
Linear ordinary differential equations with constant coefficients, simple first-order system of      202 209—211
Linear ordinary differential equations with constant coefficients, solution of, when $\Delta(\lambda)$ vanishes identically      181—182
Linear ordinary differential equations with constant coefficients, special solution of general fiist-order system of      203—205
Linear ordinary differential equations with constant coefficients, special solution of simple first-order system of      207
Linear ordinary differential equations with constant coefficients, special solution of, for standard one-point boundary problems      195—200
Linear ordinary differential equations with constant coefficients, standard one-point boundary problems with      189 190
Linear ordinary differential equations with constant coefficients, transformation of dependent variables in      159—160
Linear ordinary differential equations with constant coefficients, triangular systems of      160—162
Linear ordinary differential equations with variable coefficients, characteristic numbers for      224 226—228 230—231
Linear ordinary differential equations with variable coefficients, continuation formula for systems of      219—222
Linear ordinary differential equations with variable coefficients, existence theorems for      212—214
Linear ordinary differential equations with variable coefficients, first-order systems of      213—214 216—218 220—224 232—233
Linear ordinary differential equations with variable coefficients, fundamental solutions of      214—215 219 220 223 224
Linear ordinary differential equations with variable coefficients, indicial equation for      215
Linear ordinary differential equations with variable coefficients, iregular singularities of      215
Linear ordinary differential equations with variable coefficients, notation for system of      215
Linear ordinary differential equations with variable coefficients, ordinary points of      212
Linear ordinary differential equations with variable coefficients, Peano — Baker method for first-order system of      217—218
Linear ordinary differential equations with variable coefficients, power series solution for first-order system of      222—224
Linear ordinary differential equations with variable coefficients, regular singularities of      215
Linear ordinary differential equations with variable coefficients, simple first-order system of      216 217—218 220—222 232—233
Linear ordinary differential equations with variable coefficients, singularities of      212—215 221
Linear ordinary differential equations with variable coefficients, solution of, by collocation and GaJerkin's method      224—231
Linear ordinary differential equations with variable coefficients, solution of, by mean coeficients      232—245
Linear ordinary differential equations with variable coefficients, solution of, by method of Frobenius      215
Linear ordinary differential equations with variable coefficients, system of, reduced to first order      215—217
Linear partial differential equations, change of variables in      50—52
Linear partial differential equations, methods of collocation and Galerkin for      227
Linear substitution      23—27 64
Linear transformation, denned      26
Linear transformation, matrix of      27
Linear transformation, triangular      31
Linear vector function      258
Loading, principal directions of      265—266
MacDuffee. C.C.      51
Mass balance of aeroplane control surfaces      302
Matrices, addition and subtraction of      4
Matrices, conformable      6 9 14 25
Matrices, conjugate      33
Matrices, continued products of      9—12 221
Matrices, differentiation of      43—52
Matrices, division of      22 58—60
Matrices, elementary operations on      87—89 90 96 97
Matrices, equal      4
Matrices, equivalent      89 90—92
Matrices, fractional powers of      38 81 82
Matrices, infinite series of      40—41 53 81
Matrices, integration of      52—56
Matrices, inverse      22 see Reciprocation”
Matrices, multiplication of      6—12
Matrices, notation foi      1—3
Matrices, of differential operators      40—51 166
Matrices, partitioned      13—15
Matrices, permutabie      6 7 42 44
Matrices, predivision and postdivieion of      22
Matrices, products of      6—12
Matrices, reciprocal      22 see Reciprocation”
Matrices, representing complex scalars and quaternions      35—36
Matrices, representing finite rotation      248—249 251—254
Matrices, Taylor's theorem for      44—45
Matrices, whioh commute      6 39 42
Matrices, with null product      23—24
Matrix, adjoint      21 see
Matrix, aerodynamical stiffness      284 285
Matrix, alternate      3 33
Matrix, characteristic      64
Matrix, column      2
Matrix, D-      157
Matrix, damping      284 288 386
Matrix, definition of      1
Matrix, degeneracy of a square      18 see
Matrix, derived      43—44
Matrix, determinant of a square      10
Matrix, diagonal      3 12—13 23 66 .89 91 93
1 2 3 4
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