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| Hamilton W.R. — The collected mathematical papers. Volume 2: dynamics |
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| Предметный указатель |
Lubbock's results in lunar theory compared with Hamilton's 246 248 263 272 275 627
Lubbock, correspondence with xiii 249
Lubbock, J.W. xii xiii 238 246 248 249 250 256 257 263 264 266 274 275 276 277 278 279 283
Lubbock, Lord 249
Luminiferous aether, Hamilton's 638
Lunar tables 249 256
Lunar theory xiii 238 249. motion perturbations
Lunar theory, application of calculus of principal relations to 257 266
Lunar theory, comparison of Hamilton's, Lubbock's and Plana's results in 246 248 263 272 275 627
Lunar theory, disturbing function in, Laplace's 239 257
Lunar theory, lowering of order of approximation in 273 274
Lunar theory, method of principal function applied to xiii 238 257 266
Lunar theory, perturbational parts of elements in 242 245 247 262 268 269
Lunar theory, perturbations in, Hamilton's and Lagrange's methods compared 263 264 269 276 628
Lunar theory, principal function in 238 239
Lunar theory, principal function in, approximations to 243 247
Lunar theory, principal function in, variation of 238 239 258
Lunar theory, variational equation in 239 257
MacCullagh xii 639
Macdonald 638
Maedler 291 292
Malus 440 442
Marks of position 113 114 164 214
Marks of relative position 125
Mathematical Papers, Vol. I 3 5 105 109 168 613
Maxwell xii
Mecanique Analytique 73 74 104 106 109 117 160 163 164 165 166 622
Mecanique Celeste 9 10 11 24 51 71 264 285
Medium, crystalline, potential energy of 638. See also Crystal
Medium, dispersive See Dispersive
Medium, elastic see Elastic
Medium, resisting, approximation to S for motion in 351
Method of characteristic function, applied to dynamics x 103
Method of characteristic function, applied to three-body problem xii 1
Method of fluctuation 476 504 520 555 557
Method of integration of partial differential equations 391 634
Method of least squares 594
Method of principal function See Principal function; Principal relations calculus
Method of principal relations See Principal relations calculus
Method of variation of constants See Constants method
Method of variation of parameters See Parameters method
Method, General, in Dynamics xiii 103 162 212
Method, Hamilton's, of approximating to motion of moon 628
Methods of approximation See Approximation
Methods of determining principal function 334 335 613 631
Methods of perturbation See Perturbation
Methods, operational, applied to vibration in elastic medium xv 527
Mitscherlich 440
mobius 124 287
Mode of vibration, permanent 489 492 495 496 498 499
Mode of vibration, simple 464
Mode of vibration, sinusoidal 488 489 492 495 497
Molecules of elastic medium, vibration of 527
Molini 283
Momenta, generalised 165 214
Momenta, perturbations of 172 173
Momentary ellipse 77
Momentum, integrals of 113
Moon's coordinates, Hamilton's results compared with Lubbock's and Plana's 246 248 263 272 275 627
Moon's coordinates, perturbations of 243 245 248 262 263 272 274 277
Moon, motion of, Hamilton's method of approximating to 628
Moon, theory of xiii 238 249
Moon, theory of, application of calculus of principal relations to 257 266
Moon, theory of, comparison of Hamilton's, Lubbock's and Plana's results in 246 248 263 272 275 627
Moon, theory of, disturbing function in 238 239
Moon, theory of, lowering of order of approximation in 273 274
Moon, theory of, method of principal function applied to xiii 238 257 266
Moon, theory of, perturbational parts of elements in 242 245 247 262 268 269
Moon, theory of, perturbations in, Hamilton's and Lagrange's methods compared 263 264 269 276 628
Moon, theory of, principal function in 238 239
Moon, theory of, principal function in, approximations to 243 247
Moon, theory of, principal function in, variation of 238 239 258
Moon, theory of, variational equation in 239 257
Multiple system 150 200
Multiple system, characteristic function for, approximation to 150
Multiple system, characteristic function for, disturbing part of 153 155
Multiple system, function of elements for 209
Multiple system, integrals of undisturbed motion of 200
Multiple system, rigorous transition from binary to 155
Multiple system, with one predominant mass, perturbations of 150 155 200
Multiplicity 634
Multipliers, Lagrange's 120 121
Nearly circular orbits See Circular orbits nearly
Neptune, discovery of 104 291
Neumann 639
Newton x 104 140 208 217 231 286 288 289 290 291 597
Newtonian law of force 135 217
Newtonian law of force, hodographic representation of 287 290
Newtonian orbit x. See also Elliptic motion; Planetary motion
Node 454 456
Node, longitude of 208
Notation, Herschel's, for inverse trigonometrical functions 202
Notation, Lagrange's, for partial and total derivatives 316 317 336
Notation, Vandermonde's, for factorials 523
Operational methods, applied to vibration in elastic medium xv 527
Operator  535
Operator  530
Operator D 544
Operator I 542
Operator tan  543
Operator, Heaviside's xv 542
Optic axes of biaxal crystal 442
Orbit See also Central; Elliptic; Kepler; Newtonian; Parabolic; Planetary
Orbit, plane relative 135 136
Orbit, varying 208 209 269
Orbits, nearly circular See Circular orbits nearly
Oscillating sinusoid 497
Parabolic action 89
Parabolic motion See also Comet; Projectile
Parabolic motion, characteristic function for 139
Parabolic motion, characteristic function for, approximation to 88
Parabolic orbit 75 76
Parabolic orbit, time in 75 139 294
Parallactic inequality, approximation to 627
Parallelogram of forces, statical proof of xiii 284
Parameters, method of variation of See also Constants method
Parameters, method of variation of, applied to perturbation problem 255 279 280
Parameters, method of variation of, compared with method of principal function 255 263 269 279 280 281 282 622
Parameters, method of variation of, Poisson's mode of applying 280
Paris inch 587 591
Partial differential coefficients, Lagrange's notation for 316 317 336
Partial differential equation of first order, characteristics of xii 391 392 634
Partial differential equation of first order, complete integral of 393 396
Partial differential equation of first order, general integral of 393 396
Partial differential equation of first order, integration of 391 634
Partial differential equation of first order, integration of, Pfaffs method of 326 329 331
Partial differential equation of second order, characteristics of 636
Partial differential equation of second order, integral of 401 402
Partial differential equation of second order, integration of 397 635
Partial differential equation of second order, integration of, examples 403
Partial differential equations for function of elements 179
Partial differential equations for function of elements in multiple system 210
Partial differential equations for principal integral of differential expression 334
Partial differential equations for principal integral of total differential equation 360 365 409
Partial differential equations for Q 169
Partial differential equations for S 161 168 214 631
Partial differential equations for S, for particle 182
Partial differential equations for S, for projectile 187
Partial differential equations for S, in elliptic orbit 217 219
Partial differential equations for S, in elliptic orbit, compatibility of 219
Partial differential equations for S, in general coordinates 168 631
Partial differential equations for S, in three-body problem 230 231 233 234
Partial differential equations for V 109
Partial differential equations for V, in binary system 130
Partial differential equations for V, in central orbits 79 95
Partial differential equations for V, in central orbits, common solution of 79
Partial differential equations for V, in central orbits, transformations of 95
Partial differential equations for V, in general coordinates 116 169
Partial differential equations for V, in relative coordinates 127
Partial differential equations for V, in ternary system 142 143
| Partial differential equations for V, in three-body problem 5
Partial differential equations in motion of particle 185
Partial differential equations in motion of projectile 194
Particle, motion of 181
Particle, motion of, disturbing function for 183 185
Particle, motion of, function of elements for 185
Particle, motion of, Hamilton's equations for 182
Particle, motion of, integrals of 182
Particle, motion of, perturbation theory for 181
Particle, motion of, principal function for 182
Particle, motion of, principal function for, disturbing part of 183
Particle, motion of, varying elements for 185
Particles of aether, law of force between, xiv 448 449
Particles, linear system of See Linear system
Perihelion distance 208
Perihelion passage, time of 208
Perihelion, longitude of 208
Periodicity, degree of 485
Permanent mode of vibration of linear system 489 492 495 496 498 499
Perturbation, Lagrange's and Hamilton's methods compared 159 160 255 279 280 281 282 622
Perturbation, Lagrange's and Hamilton's methods compared, in lunar theory 263 264 269 276 628
Perturbation, problem of 171 177
Perturbation, problems of, calculus of principal relations applied to 250 257 278
Perturbation, rigorous theory of, by principal function 170 174
Perturbation, theorem of 73
Perturbation, theory of, disturbing function in 172 173
Perturbation, theory of, for motion of particle 181
Perturbation, theory of, for motion of projectile 188
Perturbation, theory of, for motion of projectile, with variation of gravity 197
Perturbation, theory of, for multiple system 150 155 200
Perturbations of dynamical system, approximations to 155 172
Perturbations of elliptic elements, in lunar theory 245 247 262 269
Perturbations of elliptic elements, in three-body problem 32
Perturbations of Jupiter 8
Perturbations of Moon See Lunar theory; Moon
Perturbations of multiple system 150 155 200
Perturbations of nearly circular orbits 30 235
Perturbations of Saturn 12
Perturbations, in three-body problem 5 20 30 231 235
Perturbations, independence of, on disturbed mass, to first order 78
Perturbations, of astronomical bodies xiii. See also Lunar theory; Three-body problem
Pfaff 326 329 331
Pfaff's method 326 329 331
Phase 459
Phase, change of 507 509 561
Phase, change of, distinguished from group-velocity xv 510 517 556 571 572 577 582 602 641
Phase, change of, velocity xii 451 556 605. velocity velocity
Phase, velocity of passage of 577 581
Phase, velocity of transmission of 459 487 491 494 496 510 517 582
Plana xiii 246 248 249 263 272 273 275 276 277 283 627
Plana's results in lunar theory, compared with Hamilton's 246 248 263 272 275 627
Plane of ecliptic 2
Plane, momentary 77
Plane, polarisation 597 598
Plane, relative orbit 135 136
Plane, waves in aether 446
Plane, waves in crystal 416
Plane, waves in crystal, velocities of propagation of 423 427 433
Planet, heliocentric coordinates of 207 208
Planet, motion of See Central orbit; Elliptic motion; Planetary motion
Planetary motion 135 217 624.
Planetary motion, characteristic function for 135
Planetary motion, principal function for 217 624
Planetary orbit, time in 139 140
Planets, known in 1834 104
Plates, phenomena of thin 597
Pleiades 291
Poggendorf 439
Point, motion of single See Particle motion
poisson xiv 109 160 163 175 177 264 276 277 280 283 419 449 536 537 614 638
Poisson brackets 175 176 201 203 204 206
Poisson brackets, constancy of 177
Poisson's criticism 614
Poisson's law of force between particles of aether 449
Poisson's mode of applying Lagrange's method of varying parameters 280
Polar coordinates, equation of living force in, for three-body problem 17 25
Polar coordinates, perturbations of nearly circular orbits in 228
Polar coordinates, perturbations of, in three-body problem 20
Polarisation plane 597 598
Polarisation, Fresnel's law of 434 444
Pontecoulant, de 249 256 264 277 283 627
Poole 542
Position, marks of 113 164 214
Position, marks of relative 125
Position, vector of 287
Potential energy of crystalline medium 638
Powell xv 439 583 595 596 599 601
Powell, correspondence with xv 583
Principal function x xiii 72 160 163 166 167 213 215
Principal function, application of, to dynamics x 162 212
Principal function, applied to perturbation theory 170 174
Principal function, approximation for nearly circular orbits 220 228 235
Principal function, approximations for projectile 189 190 191 351
Principal function, approximations in lunar theory 243 247
Principal function, approximations in three-body problem 235
Principal function, approximations to 170 335 339
Principal function, approximations to, for particle 182 183
Principal function, determination of, from complete integral 613
Principal function, determination of, Hamilton's method of 334 335 631
Principal function, disturbing part of, for particle 183
Principal function, disturbing part of, for projectile 189 190 191
Principal function, disturbing part of, in perturbation theory 170 172
Principal function, for binary system xiii 619
Principal function, for disturbed motion 171
Principal function, for elliptic orbit 217 624
Principal function, for general dynamical system 160 166 167 213 215
Principal function, for harmonic oscillator 618
Principal function, for lunar theory 238 239
Principal function, for particle 182
Principal function, for projectile 186 187
Principal function, for relative motion 200
Principal function, for three-body problem 230 231 232
Principal function, for undisturbed motion 171
Principal function, general expansion for, for nearly circular orbit 225
Principal function, integrals of motion deduced from 167 213 215
Principal function, law of variation of 160 166 213 215
Principal function, law of variation of, for elliptic orbit 217
Principal function, law of variation of, for relative motion 200
Principal function, law of variation of, in lunar theory 238 239 258
Principal function, law of variation of, in three-body problem 233
Principal function, method of See also Principal relations calculus
Principal function, method of improving approximation to 169 214
Principal function, method of, applied to lunar theory xiii 238 257 266
Principal function, method of, compared with method of varying parameters 255 263 279 280 281 282
Principal function, of total differential equations See Principal integral
Principal function, partial differential equations for 161 168 214 631
Principal function, partial differential equations for particle 182
Principal function, partial differential equations for projectile 187
Principal function, partial differential equations in elliptic orbit 217 219
Principal function, partial differential equations in three-body problem 230 231 233 234
Principal function, relation of characteristic function to 168
Principal function, relation of Q to 168
Principal functions, calculus of See Principal relations calculus
Principal integral of differential expression of first order 308 309 332
Principal integral of differential expression of first order, approximation to 335 339 631
Principal integral of differential expression of first order, approximation to, for two variables 344 348
Principal integral of differential expression of first order, determination of 334 631
Principal integral of differential expression of first order, partial differential equations for 334 409
Principal integral of system of total differential equations of any order xi 363 372
Principal integral of system of total differential equations of any order, law of variation of 363 364
Principal integral of system of total differential equations of first order 369
Principal integral of system of total differential equations of first order, law of variation of 370
Principal integral of system of total differential equations of second order 372
Principal integral of total differential equation of first order xi 305 306 316 358 365 408
Principal integral of total differential equation of first order, improvement of approximation to 367
Principal integral of total differential equation of first order, law of variation of 359
Principal integral of total differential equation, partial differential equations for 360 365 409
Principal integral of total differential equation, relation of general integral to 329 330
Principal relations, applied to lunar theory xiii 257 266
Principal relations, applied to perturbation problems 250 278
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