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| Meirovitch L. — Methods of analytical dynamics |
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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
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