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| Hamilton W.R. — The collected mathematical papers. Volume 2: dynamics |
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| Предметный указатель |
Aberration of a star, curve of 290
Academy, Royal Irish v 103 283 286 291 293
Accumulated living force 107. See also Action; Characteristic function
action 25 107 214.
Action, function, differentiation of, with respect to vis viva x xii 49
Action, law of least 108 109
Action, law of stationary 96 98 109
Action, law of varying 105
Action, law of varying, for binary system 129
Action, law of varying, for ternary system 142
Action, law of varying, for three-body problem 53 97
Action, law of varying, in general coordinates 115 120
Action, parabolic 89
Action, relative 122 125 150
Action, relative, approximate value for 151
Action, relative, law of varying 122 125
Adare, Lord 439
Aether, Faraday — Maxwell xii
Aether, Hamilton's luminiferous 638
Aether, law of force between particles of xiv 448 449
Aether, propagation of light in 446
airy 249 256 275 563
Airy's integral 563
Alcinoe 291
Amplitude 459
Amplitude, constants of 454
Angular momentum, integrals of 623
Anomaly, eccentric 43 136 624
Anomaly, true 208
Anthode xiv 293 630
Anthode of a comet 293
Anthode, relation of hodograph to 630
Anthodographic isochronism, theorem of xiv 293 630
Appell 48
Application of calculus of principal relations to lunar theory xiii 238 257
Application of characteristic function to dynamics x 103
Application of characteristic function to problem of three bodies x xii 1
Application of principal function to dynamics x 162 212
Approximate determination of elements in three-body problem 14
Approximate expression for vis viva in three-body problem 17
Approximate expressions for perturbations of multiple system 155
Approximate value of relative action 151
Approximation to motion of moon, Hamilton's method of 628
Approximation to parallactic inequality 248 272 277 627
Approximation to principal integral 335 339 344 348 367 631
Approximation to S 161 169 214 631
Approximation to S, for lunar theory 243 247
Approximation to S, for motion in resisting medium 351
Approximation to S, for nearly circular orbits 220 225 229
Approximation to S, for particle 183
Approximation to S, for projectile 189 191
Approximation to S, in three-body problem 235
Approximation to time, in three-body problem 37 612
Approximation to V 147 149 150
Approximation to V, for central orbits under various laws of force 83 88 89 92 93 94 95
Approximation to V, for multiple system 150
Approximation to V, in three-body problem 25 27 32 44 53
Approximation, lowering of order of, in lunar theory 273 274
Approximation, method of, by calculus of principal relations 250 257 278
Approximations to perturbations of dynamical system 155 172
Areal velocity 208
Areas, law of description of 112 127
Areas, law of, for binary system 134
Areas, law of, for central orbits 97
Argument of latitude 208
Astronomical bodies, perturbations of See Perturbations
Astronomical refraction 98
Asymptotic expansions of Bessel functions xii 509 539
Asymptotic values of integrals xv 539 547 554
Atmospheric refraction 96
Attracting systems, motion of 105 150 197
Attraction between particles of aether, law of xiv 448 449
Attraction, energy of 547
Auxiliary function 160. See also Principal function
Auxiliary function, approximation to 161
Auxiliary function, law of variation of 160
Auxiliary function, partial differential equations for 161
Axes, optic 442
Bays, theory of system of 105 214
Beaufort, Admiral Sir F. 103
Beaufort, D.A. 103
bessel 292 451
Bessel functions xii xv 451 458 509 511 526 547
Bessel functions, asymptotic expansions of xii 509 539
Biaxal crystal See also Dispersive crystal
Biaxal crystal, dispersion in 437
Biaxal crystal, Fresnel's law of polarisation in 434 444
Biaxal crystal, Fresnel's law of wave-velocity in 433 434 444 639
Biaxal crystal, optic axes of 442
Biaxal crystal, wave-surface in 432 442
Binary system 128
Binary system, canonical elements for 202 206
Binary system, characteristic function for xii 128
Binary system, differential equations of varying elements for 206
Binary system, integrals of motion of 132 207
Binary system, law of varying action for 129
Binary system, partial differential equation for S 619
Binary system, partial differential equations for V 130 135
Binary system, principal function for 619
Binary system, relative motion of, characteristic function for 134
Binary system, variational equation for 128
Biot 440 442
Boone 283
Born 638
Boscovich 104 118
Boscovich's hypothesis 104
Bremiker 292
British Association 256 257 267 278 410 595
Brown 240 246 248 277 627
Cajori 202 630
Calculus of principal functions See Principal relations
Calculus of principal relations See Principal relations
Calculus of quaternions See Quaternions
Calculus of variations See Variations calculus
Canonical elements xiii 202 206
Canonical equations of motion x xiii 166 215
Canonical forms of equations of motion, Lagrange's 117
Canonical set of constants 206
Capital problem of dynamics 212
Carslaw 571
Cauchy xii 277 391 413 447 448 450 469 476 516 552 561 570 578 580 583 584 585 595 596 598 601 634 638 639
Cauchy's law of dispersion 447 582 584 586 596 601
Cauchy's law of force between particles of aether 448
Cauchy's method of characteristics xii 391 634
Cauchy's principal value 469 476 516 552 580
Cauchy's researches on light-propagation in crystals, comparison with Hamilton xii 638
Cayley 104 211
Central forces, theorems on xiii 286
Central orbit See also Binary system; Elliptic motion; Planetary motion
Central orbit, approximation to V for various laws of force 83
Central orbit, characteristic function for 79
Central orbit, curvature of 100
Central orbit, hodograph of 287 288
Central orbit, partial differential equations for V in, common solution of 79
Central orbit, partial differential equations for V in, transformations of 95
Central, sun 291 292
Centre of gravity, law of motion of 112 199
Centre of gravity, motion relative to 121
Centrobaric coordinates 2 124
Centrobaric coordinates, of Jupiter and Saturn, perturbations of 20
Centrobaric radius vector, perturbations of, in three-body problem 57 67
Centrobaric velocity 199
Characteristic function xiii 105 107 214
Characteristic function, application of, to dynamics x 103
Characteristic function, applied to three-body problem xii 1
Characteristic function, approximation to 147 150
Characteristic function, approximation to, for central orbits 83 88 89 92 93 94 95
Characteristic function, approximation to, for multiple system 151 153
Characteristic function, approximation to, in three-body problem 25 27 32 44 53
Characteristic function, derivative of, with respect to vis viva x xii 46 49 108
| Characteristic function, disturbing part of, for multiple system 153 155
Characteristic function, disturbing part of, for ternary system 154
Characteristic function, for binary system xii 128
Characteristic function, for elliptic motion 44 46 135
Characteristic function, for parabolic motion 139
Characteristic function, for planetary motion 135
Characteristic function, for relative motion 121
Characteristic function, for ternary system 140
Characteristic function, for three-body problem 3
Characteristic function, integrals of motion deduced from 107 108 115
Characteristic function, law of variation of 107 168. law
Characteristic function, law of variation of, for binary system 129 131
Characteristic function, law of variation of, for relative motion 121
Characteristic function, law of variation of, for ternary system 142 143
Characteristic function, law of variation of, in general coordinates 115 120
Characteristic function, law of variation of, in three-body problem 3 4 29
Characteristic function, method of improving approximation to 147
Characteristic function, partial differential equations for 109
Characteristic function, partial differential equations for, common solution for 79
Characteristic function, partial differential equations for, in binary system 130 135
Characteristic function, partial differential equations for, in elliptic motion 45 79 138
Characteristic function, partial differential equations for, in general coordinates 116
Characteristic function, partial differential equations for, in ternary system 142 143
Characteristic function, partial differential equations for, in three-body problem 5
Characteristic function, relation of principal function to 160 168
Characteristics, Cauchy's method of xii 391 634
Characteristics, of partial differential equation of first order xii 392 634
Characteristics, of partial differential equation of second order 636
Circular hodograph, law of 288
Circular hodograph, varying 290
Circular orbits, characteristic function for 32 43
Circular orbits, nearly xiii 6 217
Circular orbits, perturbations of 30 235
Circular orbits, principal function for 218
Circular orbits, principal function for, approximations to 220 228 235
Circular orbits, principal function for, general expansion for 225
Circular orbits, principal function for, in polar coordinates 228
comet See also Parabolic motion; Planetary motion
Comet, anthode of 293
Comet, motion of 135
Common solution of partial differential equations for V 79
Comparison of Hamilton's and Lagrange's methods of perturbation 160 207 622
Comparison of Hamilton's and Lagrange's methods of perturbation, in lunar theory 269 628
Comparison of Hamilton's and Lagrange's methods, results in perturbations of three-body problem 73 77
Composition of forces, statical proof of xiii 284
Concave curvature of central orbit 100
Conies, description of, under central forces xiii 286
Constants, canonical set of 206
Constants, method of variation of 175 249. method
Constants, of amplitude and epoch 454
Constants, of cubic lattice 418
Constants, variation of elliptic, in three-body problem 32
Contact transformation 179
Convex curvature of central orbit 100
coordinates see Centrobaric; General; Geocentric; Heliocentric; Polar; Relative
Coriolis 106
Correspondence with Herschel xv 599
Correspondence with Lubbock xiii 249
Correspondence with Powell xv 583
Criticism, Jacobi's 109 613
Criticism, Poisson's 614
Crystal, biaxal, dispersion in 437
Crystal, biaxal, Fresnel's law of polarisation in 433 444
Crystal, biaxal, Fresnel's law of wave-velocity in 433 434 444 639
Crystal, biaxal, optic axes of 442
Crystal, biaxal, wave-surface in 432 442
Crystal, directions of vibration in 423 434
Crystal, dispersive, Fresnel's law of propagation in 438 444 445 639
Crystal, dispersive, wave-surface in 444
Crystal, dispersive, wave-velocity in 437 439 441
Crystal, law of vis viva for vibrations in 437
Crystal, plane waves in, conditions for 416
Crystal, plane waves in, velocity of 423 427 433
Crystal, wave-velocities in 423
Crystalline medium, potential energy of 638
Crystals, optical properties of, comparison with Cauchy's and Green's results 638
Crystals, propagation of light in xii xiv 413 450
Crystals, reflection and refraction in 435
Cubic lattice 418 450
Curvature of central orbit 100
Darkness, dynamics of xii 541 555 599 600
Degree of periodicity 485
Depression of order of approximation, in lunar theory 273 274
Derivatives, Lagrange's notation for partial and total 316 317 336
Description of areas, law of See Areas
Description of conies and sphero-conies under central forces xiii 286
Description of wave-motion in elastic medium 563 604 640
Determination of principal function 613 631
Determination of principal function, approximate 335 339
Determination of principal function, conditions for 334 335 409
Development of theoretical dynamics 104
Differential equations See Partial; Total differential equations
Differential expression of first order, calculus of principal relations for 332
Differential expression of first order, principal integral of 308 309 332
Differential expression of first order, principal supplementary equations of 333
Diffraction 569
Diffraction, spectrum 591
Direction of light vector xii
Directions of vibration in crystal 423 434
Dispersion, in biaxal crystal 437
Dispersion, law of 447 582 584 586 596 601
Dispersion, of light 578 583 586
Dispersion, prismatic 594
Dispersive crystal See also Biaxal crystal
Dispersive crystal, law of wave-propagation in 438 444 445 639
Dispersive crystal, wave-surface in 444
Dispersive crystal, wave-velocity in 437 439 441
Dispersive medium, law of wave-velocity in 447 582 584 586 596 601
Dispersive medium, propagation of vibration in 437 446 569 572 578 583 596
Dispersive medium, three-dimensional waves in 569
Disturbed motion, principal function for 171
Disturbing function, for particle 183 184
Disturbing function, for projectile 189
Disturbing function, in general perturbation theory 172 173
Disturbing function, in lunar theory, Laplace's 239 257
Disturbing function, in three-body problem 32 34 44 49 53 231 232
Disturbing function, in three-body problem, approximation to 49 237
Disturbing function, in three-body problem, Hamilton's and Laplace's compared 51
Disturbing function, in three-body problem, heliocentric 70
Disturbing function, in three-body problem, law of variation of 37
Disturbing part of S 170 172
Disturbing part of S, for particle 183
Disturbing part of S, for projectile 189 190 191
Disturbing part of V, for multiple system 153 155
Disturbing part of V, for ternary system 154
Donkin 206
Donkin's theorem 206
Dublin, University of 283
Dunraven Castle 238
Dynamics, application of characteristic function to x 103
Dynamics, application of principal function to x 163 212
Dynamics, capital problem of 212
Dynamics, development of theoretical 104
Dynamics, fundamental theorem of 3
Dynamics, general Method in xiii 103 162 212
Dynamics, of darkness xii 541 555 599 600
Dynamics, of light xii 411
Dynamics, of material bodies 1
Dynamics, reciprocal theorem in xv 451 458 490 493
Earth's annual motion, hodograph of 290
Eccentric anomaly 43 136 624
Eccentricity, vector of 290
Elastic medium, description of wave-motion in 563 604 640
Elastic medium, energy of attraction between particles of 547
Elastic medium, equations of vibration in 527
Elastic medium, equations of vibration in, general integral of 547 548 576 601 602
Elastic medium, propagation of motion in xv 527 599
Elastic medium, three-dimensional waves in 569
Elastic medium, two-dimensional waves in 568
Element of contact 634
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