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Meirovitch L. — Methods of analytical dynamics
Meirovitch L. — Methods of analytical dynamics

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Название: Methods of analytical dynamics

Автор: Meirovitch L.

Язык: en

Рубрика: Физика/Классическая физика/Теоретическая механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 524

Добавлена в каталог: 29.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute integral invariant      347
Acatastatic system      51
Acceleration, absolute      11
Acceleration, centripetal      112
Acceleration, Coriolis      112
Acceleration, relative      112
Action and reaction      10 22
Action integral      3
Action variables      365—373
Adjoint equation      215
Affine transformation      181 409
Angle variables      365—373
Angular momentum, apparent      24
Angular momentum, conservation of      13 24 27 415
Angular momentum, matrix      108 129
Angular momentum, of rigid body      126—130
Angular momentum, of system of particles      23
Angular momentum, of the earth      113
Angular momentum, translation theorem for      130—132
Angular velocity      43 108
Angular velocity, in terms of body axes      142
Angular velocity, in terms of node-axis system      142
Angular velocity, vector      108
Anomaly, eccentric      43 409
Anomaly, mean      43 409
Anomaly, true      409
Antecedents      494
Aphelion      33
Apocentron      33
Apogee      33
Apsis      33
Arc, closed      505
Arc, open      505
Ascending node      412
Ascending node, longitude of      412
Asymptotic stability      176
Asymptotic stability, of linear autonomous system      222
Asymptotic stability, orbital      177
Asymptotic stability, uniform      176
Atmospheric drag, effect on satellite orbits      463—466
Atmospheric drag, effect on stability of artillery shells      255—258
Attitude motion of satellites      466—483
Attitude motion of satellites, gravity-gradient stabilized      467 470—475
Attitude motion of satellites, spin stabilized      475—483
Autonomous systems      174 209 217—224
Autonomous systems, linear      217—224
Autonomous systems, linear, asymptotically stable      222
Autonomous systems, linear, stable      222
Autonomous systems, linear, unstable      222
Averaging, method of      322—326
Averaging, operator      323
Averaging, principle of      324
Axial vector      110
Barbasin and Krasovskii's theorem on asymptotic stability      237 241
Barycenter      414
Bendixson's criterion      205
Body axes      124
Body cone      144
Boundary of set      503 504
Bounds of libration of satellites      481
Brachistochrone problem      55
Canonical systems      94 172
Canonical systems, stability of      243—252
Canonical systems, variational equations from      229—231
Canonical transformations      See Contact transformations
Catastatic system      51
Catenary      59 64
Cauchy — Lipschitz theorem      174 176 179
Center of gravity      21
Center of mass of rigid body      127
Center of mass of system of particles      21
Center, as singular point      184 186 191
Central force      25—40
Centrifugal force      34 77
Centrifugal potential      34
centripetal acceleration      112
Characteristic determinant      180 218 222
Characteristic equation      180 222.
Characteristic equation, eigenvalues of, or roots of      181 222
Characteristic exponents      266
Characteristic exponents for canonical systems with periodic coefficients      275
Characteristic in motion space      174
Characteristic multipliers      266
Characteristic multipliers, simple      267
Characteristic polynomial      218. See also Characteristic equation)
Characteristic polynomial, elementary divisor of      218
Characteristic polynomial, invariant coefficients of      218
Characteristic polynomial, simple      218
Characteristic velocity      491
Chasles'theorem      126
Chetayev's instability theorem      236 241 291
Class of a function      11 174
Closed domain      506
Closed interval      502
Closed set      503
Closed sphere      502
Combination tones      321
Complementary Kronecker delta      22 414
Complete damping      247
Complete degeneracy      370 372
Complete equations      180
Complete equations, stability of      186
Conditionally periodic motion      369. See also Multiply periodic motion
Configuration space      46 172
Congruence      1 2 497
Consequents      494
Conservation of angular momentum      13 24 27 415
Conservation of energy      16 66 84 416
Conservation of generalized momentum      82
Conservation of linear momentum      12 23
Conservative force field      See Conservative system
Conservative system      15 16
Conservative system, canonical      243—247
Conservative system, motion in the large      189—194
Conservative system, with ignorable coordinates      249—250
Constraint, force of      48 62
Constraint, force of, work performed by      49—50
Constraint, holonomic      51 55
Constraint, inequality      51
Constraint, kinematical      47 48
Constraint, nonholonomic      51 54
Constraint, scleronomic      51
Constraint, system with      48—52
Contact transformations      334—346 373
Contact transformations, homogeneous      338
Contact transformations, infinitesimal      352—354
Continuity      497 500 505
Contraction hypothesis      6
Control surface      483
Control volume      483
Coordinate system      See Reference system or frame
Coordinate transformation      46 102—104
Coordinates, cyclic      82 97 149. ignorable
Coordinates, generalized      47
Coordinates, ignorable      82 85—88 249. cyclic
Coriolis acceleration      112
Coriolis effect      115
Coriolis force      4 8 77
Coriolis force in variable-mass systems      486 488
Coulomb force field      37
Coulomb force field, scattering in      37—40
Critical behavior      187 222
Critical behavior of linear autonomous system      222
Critical behavior of variational equations with periodic coefficients      272
Critical point      179
Curves of zero relative velocity      477
Cuspidal motion      153
Cyclic characteristic      See Limit cycle
Cyclic coordinate      82 97 149.
Cyclic trajectory      195 198.
Cyclic trajectory, adjacent      204
Cyclone      115
Cylindrical region      175
D'Alembert's principle      65—66
D'Alembert's principle, generalized      65
Damping, coefficient of      90 188
Damping, complete      247
Damping, pervasive      248
Decrescent function      290
Degeneracy, complete      370 372
Degeneracy, m-fold      370
Degrees of freedom      46—48
Degrees of freedom of a rigid body      123
Descending node      412
Determinant, characteristic      180 218 222
Determinant, Jacobian      180 336 348
Determinant, of a matrix      104 185 219
Dirac delta function      385 387
Direct method of Liapunov      See Liapunov's direct or second method
Direct precession      146
Displacement, actual      48
Displacement, possible      48
Displacement, virtual      50 53
Displacement, virtual, reversible      60
Dissipation function      See Rayleigh's dissipation function
Dissipative forces, of Rayleigh type      88—91
Dissipative forces, stability in the presence of      252—258
Distance between a point and a set      177 502
Distance between points      501
Distance between sets      502
Disturbing function      428—430
Disturbing function, due to gravitational field of oblate planet      460—461
Disturbing function, resolution of      447—450
Domain of attraction      176 236
Domain, closed      506
Domain, convex      506
Domain, open      506
Double pendulum      78—79
Duffing's equation      313—322
Dyad      495
Dyadics      494—496
Dyadics, conjugate      494
Dyadics, double dot product of      496
Dyadics, inertia      133 137 496
Dyadics, scalar product of vector and      494
Dyadics, symmetric, or self-conjugate      494 496
Dyadics, unit, or identity      495
Eccentric anomaly      43 409
Eccentricity      33 411
Ecliptic plane      412
Effective force      65
Eigenvalue problem      124
Eigenvalues      124
Eigenvalues, multiplicity of      218
Eigenvalues, nullity of      218
Eigenvectors      124
Einstein, general relativity theory or gravitational theory of      2 8 11
Einstein, special relativity theory of      2 7
Element of a set      498
Element of a set, greatest lower bound      501. See also Infimum
Element of a set, image of      500
Element of a set, inverse image of      500
Element of a set, least upper bound      501. See also Supremum
Element of a set, lower bound      501
Element of a set, maximal      500
Element of a set, upper bound      501
Ellipsoid of inertia      136
Elliptical three-body problem      425
Energy      14—17
Energy diagram      17—21
Energy integral      151 190 416
Energy, conservation of      16 66 84 85 416.
Energy, total      16
Epsilon symbol      109
Equations of motion for quasi-coordinates      157—160
Equations of motion for relative motion      428—430
Equations of motion in terms of arbitrary axes      160—162
Equations of motion of Euler      138—140 143 147
Equations of motion of Hamilton      91—97
Equations of motion of Lagrange      72—81 90
Equations of motion of Newton      10—11 13
Equilateral-triangle solution in general three-body problem      419
Equilateral-triangle solution in restricted three-body problem      424
Equilibrium point      174. See also Singular point
Equilibrium point, at the origin      175 227
Equilibrium point, neighborhood of      175 179
Equilibrium point, stability of      176
Equilibrium position, static      59 62.
Equivalent force in variable-mass systems, Coriolis      486 488
Equivalent force in variable-mass systems, due to unsteadiness of relative motion      486 488
Equivalent force in variable-mass systems, reactive      486 489
Equivalent potential energy      See Modified potential energy)
Escape velocity      35
Ether, luminiferous      5 6
Euclidean distance      501
Euclidean geometry      1 2
Euclidean norm or length      175 502
Euclidean space      2 172 175 211 501
Euler — Lagrange differential equation      57
Euler's angles      140—143
Euler's equations of motion      138—140 143 147
Euler's equations of motion, modified      140
Euler's theorem on homogeneous functions      84
Euler's theorem on motion of rigid bodies      126
Extended Hamilton's principle      68
Extended Liouville's theorem      343
Extremum      53
First integrals of motion      82 249
First point of Aries      412 438
First-approximation equations      180
First-approximation equations, Liapunov's theorem on      226—229
First-approximation equations, stability of      187
Floquet's theory      264—270
Floquet's theory, applied to second-order systems      278 280
Focus      See Spiral point
force      1 2
Force field, conservative      15
Force field, lamellar, or irrotational      17
Force, aerodynamic      255 489
Force, applied, or impressed      60
Force, body      485
Force, central      25
Force, centrifugal      4 8 34 77
Force, conservative      15
Force, Coriolis      4 8 77 486
Force, Coulomb      37
Force, dissipative      88
Force, due to unsteadiness of relative motion      486
Force, effective      65
Force, external      21
Force, friction      15
Force, generalized      61
Force, gravitational      8
Force, gyroscopic      77
Force, impulsive      79—81
Force, inertia      65
Force, internal      21
Force, nonconservative      17 83
Force, nonpotential      17
Force, of constraint      48 62
Force, potential      17
Force, reactive      486
Force, restoring      18
Force, surface      485
Foucault's pendulum      101 116—119
Free variation      54
Frequencies of gyrocompass      396
Frequencies of gyrocompass, damped      397
Frequencies, multi-degree-of-freedom system      368 370 373
Frequencies, multi-degree-of-freedom system, commensurable      369
1 2 3 4
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