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| Meirovitch L. — Methods of analytical dynamics |
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| Предметный указатель |
Newton, laws of 4 9
Newton, laws of, first law 4 9
Newton, laws of, gravitation law 4 11 12.
Newton, laws of, second law 9 11
Newton, laws of, third law or law of action and reaction 10 22
Nodal axis 140 412
Node in orbital motion, ascending 412 438
Node in orbital motion, ascending, longitude of 412
Node in orbital motion, descending 412
Node, as singular point, degenerate 183
Node, as singular point, degenerate, stable 182 183 185
Node, as singular point, degenerate, unstable 182 185
Nonautonomous system 174 263
Nonautonomous system, linear with periodic coefficients 264—270 309—313
Nonautonomous system, linear with periodic coefficients, asymptotically stable 268
Nonautonomous system, linear with periodic coefficients, perturbation solution of 309—313
Nonautonomous system, linear with periodic coefficients, reducible 270
Nonautonomous system, linear with periodic coefficients, stable 269
Nonautonomous system, nonlinear 313—327
Nonautonomous system, unstable 269
Nonautonomous system, weakly 294
Nonconservative systems 17 80
Nonconservative systems, Hamilton's equations for 95
Nonconservative systems, Hamilton's equations for, stability of 247—249
Nonconservative systems, Lagrange's equations for 76 88—91
Nonholonomic constraint 51 54
Nonholonomic system 51 162—164
Nonhomogeneous system 216 221
Noninertial system of reference 101 104 112
Nonlinear spring, hard 207
Nonlinear spring, soft 207 260
Nonlinear systems or equations 170—171 190 198 209 293 300
Nonlinear systems or equations, behavior of 187 227
Nonlinear systems or equations, nonautonomous 313—327
Nonlinear systems or equations, perturbation solution of 294—297 299—309 313—327
Nonlinear systems or equations, weakly 294
Nonnatural system 77 87
Nonnatural system, stability theorem for 247
Nonpotential forces 17
Norm, Euclidean 175 502
Null solution 176. See also Trivial solution
Nutation 142 152
Nutation of earth's polar axis 438—442
Oblate planet, effect of gravitational field of 457—463
Open domain 175
Open interval 502
Open set 503
Open set, connected 176
Open sphere 502
Orbit, circular 33 36
Orbit, determination of 409—413
Orbit, eccentricity of 33
Orbit, elliptic 33 35 409
Orbit, equation of 32
Orbit, hyperbolic 33 34 38
Orbit, inclination of 412
Orbit, Keplerian 409 442 453 457
Orbit, modification of 453
Orbit, of planet 30—37
Orbit, of satellite 30—37
Orbit, open 34
Orbit, osculating 444
Orbit, parabolic 33 34
Orbit, perturbation of 457—466
Orbit, rendezvous 455
Orbit, transfer 453—457
Orbital elements 41 442—446 454
Orbital elements, change of 453—457
Orbital elements, osculating 444
Orbital elements, variation of 442—446
Orbital reference frame 467
Orbital stability 177 272—273
Orbital stability, asymptotic 273
Ordinary point 174. See also Regular point
Orthogonal axes 104
Orthogonal transformation 124. See also Orthonormal transformation
Orthonormal transformation 103 109 134 344
Oscillator, harmonic 17 360—361 370—371
Oscillator, harmonic, anisotropic 379
Oscillator, harmonic, natural frequency of 19
Oscillator, harmonic, period of 19
Osculating elements 444
Osculating orbit 444
Path in the configuration space 67
Pendulous weight 394
Pendulum, double 78—79
Pendulum, of Foucault 101 116—119
Pendulum, simple 187—189 365
Pendulum, spherical 84—85 87—88 96—97
Pendulum, with moving support 287—288
Pendulum, with moving support, damped 325—327
Pericentron 33
Perigee 33
Perigee, height 35
Perihelion 33
Periodic matrix 264 270
Periodic solution 269 365
Periodic solution of Duffing's equation 313—322
Periodic solution of Hamilton's equations 273—277
Periodic solution of Hill's equation 279
Periodic solution of Mathieu's equation 282—287
Periodic solution, stability of 271—273
Periodicity conditions 301 314
Perturbation 175 225 293 294
Perturbation method 293
Perturbation method, averaging method 322—326
Perturbation method, based on Hamilton — Jacobi theory 372—377
Perturbation method, based on Hill's determinants 309—313
Perturbation method, fundamental technique 294—297
Perturbation method, Krylov — Bogoliubov — Mitropolsky 302—309
Perturbation method, of Lindstedt 299—302
Perturbative function See Disturbing function
Perturbed motion, differential equations of 175 225
Pervasive damping 248
Pfaffianform 48 51
Phase plane 178
Phase portrait 173
Phase space 173
Picard — Lindelof theorem 216
Poincare stability 177. See also Orbital stability
Poincare — Bendixson theorem 199—204
Poincare's relative integral invariant 348
Poinsot's geometric description 147—149
Point of a set 501
Point of a set, boundary 503 504
Point of a set, interior 503
Point of a set, isolated 505
Point of a set, limit or accumulation 503 504
Point of a set, neighborhood of 503
Poisson brackets 349—352
Polhode 149
Positive definite function 232 289
Positive definite matrix 232
Positive semidefinite function 232 289
Postfactor 495
potential energy 15 32 61
Potential energy, augmented 61
Potential energy, gravitational 32 416 430—438 460
Potential energy, modified or equivalent 32 88 247 418 422
Potential function 17
Precession 142 152
Precession of earth's polar axis 438—442
Precession of the equinoxes 438 441
Precession, direct 146
Precession, fast 156
Precession, retrograde 146
Precession, slow 156
Precession, steady 155—156
Prefactor 494
Principal axes 134—137
| Principal matrix 213
Principal minor determinants 233
Principal moments of inertia 136
Principle of d'Alembert 65—66
Principle of d'Alembert, generalized 65
Principle of Hamilton 66—72
Principle of Hamilton, extended 68
Principle of least action 69 330—334
Principle of virtual work 59—64
Products of inertia 129
Pseudovector 110
Quadratic form, homogeneous 74 137 232
Quadric surface 136
Quasi-coordinates 139 157
Quasi-coordinates, Lagrange's equations for 157—160
Quasi-harmonic system 298 301
Quasi-linear system 294
Rayleigh's dissipation function 88—91 95 248
Reducible system 270
Reference system or frame 2 3
Reference system or frame, heliocentric 412
Reference system or frame, inertial or Galilean 3 9
Reference system or frame, noninertial 112
Reference system or frame, orbital 467
Reference system or frame, rotating 104—119
Reference system or frame, rotating, motion relative to 110—119
Region 175 506
Region, cylindrical 175
Region, spherical 175 502
Regular point 174 179
Relative motion, equations of 428—430
Relativistic mass 8
Relativity principle of Galileo 3
Relativity theory of Einstein, general or gravitational 2 8 11
Relativity theory of Einstein, special 2 7
Representative point 46 172
Repulsive central force See Scattering in inverse square field
Retrograde precession 146
Rheonomic system 51
Riemannian geometry 2
Riemannian space 8
Rigid body 122
Rigid body, angular momentum of 126—130
Rigid body, center of mass of 127
Rigid body, equations of motion for 137—138
Rigid body, equations of motion for, arbitrary axes 160—162
Rigid body, kinematics of 123—126
Rigid body, kinetic energy of 132—134
Rigid body, kinetic energy of, rotational 133
Rigid body, kinetic energy of, translational 133
Rigid body, linear momentum of 123—126
Rocket dynamics 487—491
Rolling of a coin 162—164
Rotating reference system 104—110
Rotation, finite 106
Rotation, improper 110
Rotation, infinitesimal 107
Rotation, matrix 105 141
Rotation, proper 110
Routh — Hurwitz criterion 222—224
Routh's method for ignoration of coordinates 83 85—88
Routh's theorem 250
Routhian 86 151 249
Rutherford's scattering formula 39
Saddle point 182 186 191
Satellite orbit 30—37
Satellite orbit, perturbation of 457—466
Satellite orbit, perturbation of, by atmospheric drag 463—466
Satellite orbit, perturbation of, by gravitational field of oblate planet 457—463
Satellite orbit, perturbation of, long-period 461 462
Satellite orbit, perturbation of, secular 461 462
Satellite orbit, perturbation of, short-period 461 462
Satellite orbit, regression of the nodes 459
Satellite rotational motion See Attitude motion of satellites
Scattering in inverse square field 37—40
Scattering in inverse square field, angle 38
Scattering in inverse square field, fixed center of force 37
Scattering in inverse square field, for total cross section of 40
Scattering in inverse square field, moving center of force 40
Scattering in inverse square field, Rutherford formula for 39
Schuler period 403
Schuler tuning 398—403
Scleronomic system 51
Second method of Liapunov See Liapunov's direct or second method
Secular perturbation of satellite orbit 461 462
Secular terms 294 297—299
Segment See Interval closed
Segment without contact 200
Self-adjoint system 215
Self-excited oscillation 199
Self-sustained oscillation 199
Semimajor axis of ellipse 36
Semiminor axis of ellipse 410
Separable systems 361—365
Separation of variables 361 372
Separatrix 193
Set(s), boundary of 503 504
Set(s), bounded 502
Set(s), cartesian product or direct product of 500
Set(s), closed 503 504
Set(s), closure of 504
Set(s), compact 505
Set(s), complement of 499
Set(s), connected 175 506
Set(s), connected, arcwise 498
Set(s), connected, simply 498
Set(s), dense 504
Set(s), diameter of 502
Set(s), difference of 499
Set(s), disjoint 499
Set(s), distance between 502
Set(s), empty, null, or void 499
Set(s), interior of 503
Set(s), intersection of 499
Set(s), isolated point of 505
Set(s), limit point of, or accumulation point of 503 504
Set(s), open 503 504
Set(s), partially ordered 500
Set(s), union of, or sum of 499
Short-period perturbation of satellite orbit 461 462
Significant behavior 222
Significant behavior of linear autonomous systems 222
Significant behavior of variational equations with periodic coefficients 272
Similarity transformation 125 181 218 266
simple pendulum 187—189 365
Simply periodic motion 366
Simultaneity 4
Simultaneity, absolute 7
Simultaneity, relative 8
Single-axis gyroscope 403
Singular point 174. See also Equilibrium point
Singular point, at the origin 175
Singular point, center, or vortex 184
Singular point, isolated 175
Singular point, node 182
Singular point, node, degenerate 183
Singular point, nonelementary 192
Singular point, saddle point 182
Singular point, spiral point, or focus 184
Sleeping top 156
Sleeping top, stability analysis by Liapunov's direct method 251—252
Solidification, principle of 487
Space 1 8
Space cone 144
Space, absolute 2 4
Space, configuration 46 172
Space, Euclidean 2 175 211 501
Space, inertial 3
Space, Minkowski, or world 7 8
Space, phase 173
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