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| Hamilton W.R. — The collected mathematical papers. Volume 2: dynamics |
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| Предметный указатель |
Elements, approximate determination of, in three-body problem 14
Elements, canonical xiii 202 206
Elements, elliptic 30 43 104 202
Elements, elliptic, perturbations of, in lunar theory 245 247 262 269
Elements, elliptic, perturbations of, in three-body problem 32
Elements, function of 163 177 179
Elements, function of, approximations to 180
Elements, function of, for multiple system 209
Elements, function of, for particle 185
Elements, function of, for projectile 193 196
Elements, function of, law of variation of 179
Elements, function of, partial differential equations for 179 185 194 210
Elements, Lagrange's 163
Elements, method of variation of 174 622
Elements, of undisturbed motion 174 200
Elements, varying 163 174 177 209
Elements, varying, differential equations of 175 201 206
Elements, varying, for binary system 206
Elements, varying, for multiple system 200
Elements, varying, for particle 185
Elements, varying, for projectile 192
Elements, varying, in three-body problem 77
Ellipse, fixed 57 628
Ellipse, Hamilton's 208 209 266 269 628
Ellipse, Lagrange's 209 269 628
Ellipse, momentary 77
Ellipse, varying 208 209 269
Elliptic elements 30 43 104 202
Elliptic elements, perturbations of, in lunar theory 245 247 262 269
Elliptic elements, perturbations of, in three-body problem 32
Elliptic motion 43 135 217 624
Elliptic motion, characteristic function for 44 46 135
Elliptic motion, principal function for 217 624
Elliptic orbit, longitude in 208
Elliptic orbit, time in 139 140
Elliptic variations, in three-body problem 34
Energy 106. See also Living force; Vis viva
Energy of attraction between particles of elastic medium 547
Energy of vibrating system 463
Energy, potential, for crystalline medium 638
Ephemerides 256
Epoch 459
Epoch, constants of 454
Equation of limits 309
Equation of limits, variational, for binary system 128
Equation of limits, variational, for ternary system 140
Equation of limits, variational, in lunar theory 239 257
Equation of limits, variational, Lagrange's 105 164 212
Equations See also Partial; Total differential equations; Principal supplementary equations
Equations of motion, Hamilton's xiii 166 215
Equations of motion, Hamilton's, for particle 182
Equations of motion, Hamilton's, for projectile 186
Equations of motion, Lagrange's 117 164
Equations of motion, transformation of 164
Equations of vibration, in elastic medium 527
Equations of vibration, in elastic medium, general integral of 547 548 576 601 602
Equations of vibration, of attracting or repelling system 413 446 569 578
Equations of vibration, of linear system of particles 452 576 600
Equations, canonical x xiii 166 215
Equivalent vibrations, principle of 437
Euclid 289
Euler 139
Euler's theorem 139
Extinction, velocity of 571
Factorials, Vandermonde's notation for 523
Faraday xii
Faraday — Maxwell aether xii
fit 597
Five points in space, relation connecting 146
Fixed ellipse 57 628
Fixed sinusoid 502
Fluctuating functions xii xv 451 458 504 520 557
Fluctuation, method of 476 504 520 555 557
Fluctuation, principle of 520 581
Foci, kinetic 78
Force between particles of aether, law of xiv 448 449
Force, approximation to V for various laws of 83 88 89 92 93 94 95
Force, living See Living force; Vis viva
Force, Newtonian law of 135. See also Planetary motion
Force, Newtonian law of, hodographic representation of 287 290
Force-function 106 164 198
Force-function for binary system 128
Force-function for ternary system 140
Forces, central, theorems on xiii 286
Forces, parallelogram of, statical proof xiii 284
FOURIER 529 579
Fourier's theorem 529 579
Fraunhofer 587 588 589 590 591 592 593 594
Fresnel 432 433 434 438 439 444 445 595 639
Fresnel's law of polarisation in biaxal crystal 434 444
Fresnel's law of propagation in dispersive crystal 438 439 444 445 639
Fresnel's law of wave-velocity in biaxal crystal 433 434 444 639
Fresnel's wave-surface 432 442
Function See Action; Bessel; Characteristic; Disturbing; Elements function
Fundamental theorem of calculus of principal relations 363 364
Fundamental theorem of dynamics 3
Galileo 104
Gamma function 508
General coordinates 113 118 164 214
General coordinates, characteristic function in 115 167 168
General coordinates, equations of motion in 117 164
General coordinates, Hamiltonian function in 165 215
General coordinates, integrals of motion in 115 167 215
General coordinates, law of varying action in 115 120 125
General coordinates, partial differential equations for for V in 116 169
General coordinates, partial differential equations for S in 168 631
General coordinates, principal function in 166 215
Geocentric coordinates of moon 238
Geocentric longitude of moon 240
Geocentric longitude of moon, perturbations of 243 245 248 262 263 272 274 277
Geocentric radius vector of moon 240
Geocentric radius vector of moon, perturbations of 243 245 248 262 263 272 274 277
Goursat 635 636 637
Grating 591
Graves, C. 286
Graves, R. P. 104 106 297 599 607
Gravity, centre of See Centre of gravity
Gravity, motion under See Projectile
Green 638
Group-velocity xii. See also Velocity of progress of vibration; Velocity of propagation of disturbance; Velocity of propagation of vibration
Group-velocity, distinguished from phase-velocity xv 510 517 556 571 572 577 582 605 641
H-function See Hamiltonian function; Living force; Vis viva
Halley 585
Hamilton integral 614
Hamilton's ellipse 208 209 266 269 628
Hamilton's equations of motion x xiii 166 215
Hamilton's luminiferous aether 638
Hamilton's principle 167
Hamilton's theorem on central orbits xiii 286
Hamilton, life of 104 106 297 599 607
Hamiltonian function 165 215
Hamiltonian function, law of variation of 215
Harmonic oscillator, principal function for 618
Heat, effect of, on indices of refraction 440
Heaviside xv 542
Heaviside's operator xv 542
Heliocentric coordinates 51 53 70 207 208
Heliocentric coordinates, perturbations of, in three-body problem 24 70 71 72
Heliocentric disturbing function 70
Heliocentric longitude of Saturn's 14
Heliocentric longitude, perturbations of Jupiter's 11
Heliocentric plane, perturbation of coordinate perpendicular to 77
Heliocentric radius vector, of Jupiter's 11
Heliocentric radius vector, of Saturn's 14
Heliocentric radius vector, perturbations of 71
Heliocentric velocity 208
Herschel's notation for inverse trigonometrical functions 202
Herschel, correspondence with xv 599
Herschel, Miss C. 607
Herschel, Sir J. xv 202 527 589 593 599 607
| Hodograph xiii 287
Hodograph, law of circular 288 293
Hodograph, momentary relative 291
Hodograph, of central orbit 287 288
Hodograph, of earth's annual motion 290
Hodograph, relation of anthode to 630
Hodograph, relative 290
Hodograph, varying circular 290
Hodographic isochronism, theorem of xiv 293 630
Hodographic representation of moving point 289
Hodographic vector 291
Hodographs, reciprocal 288
Houel 211
Hypersurface 617
Hypothesis, Boscovich's 104
I, operator 542
Iceland Spar, double wave-surface in 441
Iceland Spar, indices of refraction of ordinary ray in 439 440
Iceland Spar, velocity of light in 439 441 442
Indices of refraction, effect of heat on 440
Inequality, parallactic, approximation to 248 272 277 627
Infinite linear system, vibration of doubly, recapitulation of results 495
Infinite linear system, vibration of doubly- 458 459 460 461 465 482 502 503 511
Infinite linear system, vibration of semi- 457 459 460 461 465 482 500 511
Infinite linear system, vibration of semi-, recapitulation of results 492
Integral of partial differential equation of second order 401 402
Integral, Airy's 563
Integral, complete, determination of principal function from 614
Integral, complete, of partial differential equation of first order 393 396
Integral, general, of partial differential equation of first order 329 330 393 396 401 402
Integral, general, of partial differential equation of first order, connection with principal integral of total differential equation 329 330
Integral, Hamilton 614
Integral, principal See Principal integral
Integral, relation, principal See Principal integral
Integrals of momentum 113
Integrals of motion for binary system 132 133
Integrals of motion for particle 182
Integrals of motion for projectile 186
Integrals of motion, deduced from from S 167 213 215
Integrals of motion, deduced from from V 108 115
Integrals of motion, deduced from Q 167
Integrals of motion, verification of 109
Integrals of undisturbed motion 171 174
Integrals of undisturbed motion, for binary system 202
Integrals of undisturbed motion, for multiple system 200
Integrals of undisturbed motion, for particle 183
Integrals of undisturbed motion, for projectile 188 189
Integrals, asymptotic values of xv 539 547 554
Integration of partial differential equations, by calculus of principal relations xii xiv 391 634
Integration of partial differential equations, by Pfaff's method 329 331
Interference of polarised rays 598
Interference, phenomena of 591 596
Interference, spectrum of 591
Interval of wave 421
Inverse of hodograph, anthode as 630
Inverse trigonometrical functions, Herschel's notation for 202
Inversion, method of 630
Irish Academy, Royal v 103 283 286 291 293
Isochronism, hodographic and anthodographic xiv 293 630
Isotropic medium 638 639
jacobi 48 109 168 206 283 613 614
Jacobi's criticism 109 613
Jeffreys 542
Jupiter's centrobaric longitude, perturbations of 10 11
Jupiter's centrobaric longitude, radius vector, perturbations of 9 10
Jupiter's heliocentric longitude, perturbations of 11
Jupiter's heliocentric longitude, radius vector, perturbations of 11
Jupiter, equations of motion of 2
Jupiter, perturbations of 8
Jupiter, perturbations of, agreement with Laplace 11
Jupiter, perturbations of, in centrobaric coordinates 20
Jupiter, perturbations of, in heliocentric coordinates 70
Kelvin 561
Kepler x 290
Kepler orbit x. See also Planetary motion
Kinetic foci 78
Known planets in 1834 104
Lagrange x 53 73 74 77 104 105 106 108 109 117 118 121 160 163 164 166 167 175 209 212 213 255 263 266 269 276 279 280 282 283 316 317 331 336 613 614 622 629
Lagrange's elements 163
Lagrange's ellipse 209 269 629
Lagrange's equations of motion 117 164
Lagrange's method of variation of parameters, applied to perturbation problem 255 279 280
Lagrange's method of variation of parameters, co mpared with method of principal function 255 263 269 279 280 281 282 622
Lagrange's multipliers 120 121
Lagrange's notation for partial and total derivatives 316 317 336
Lagrange's results in perturbations of three-body problem, compared with Hamilton's 77
Lambert 139
Lambert's theorem 139
Laplace x 8 11 12 49 51 105 109 519 563
Laplace, agreement with, in lunar theory 239 257
Laplace, agreement with, in perturbations of Jupiter 11 Laplace's disturbing function compared 51
Latitude, argument of 208
Lattice, cubic 418 450
Law of circular hodograph 288 293
Law of description of areas See Areas
Law of dispersion 447 582 584 586 596 601
Law of force between particles of aether xiv 448 449
Law of living force 107
Law of motion of centre of gravity 112 199
Law of polarisation in biaxal crystal, Fresnel's 434 444
Law of propagation in dispersive crystal, Fresnel's 438 439 444 445 639
Law of variation See Action function; Characteristic function; Disturbing function; Elements function
Law of wave-velocity in biaxal crystal, Fresnel's 433 439 444 445 639
Laws of least, stationary, varying action See Action
Le Verrier 292
Le Verrier's planet 292
Least action, law of See Action
Least squares, method of 594
legendre 508 627
Legendre's celebrated function 508
Legendre's polynomials 9 240 258 627
Leibniz 106
Length of undulation 446
Length, wave- 446
Life of Hamilton 104 106 297 599 607
Light See also Crystals; Propagation; Reflection; Refraction; Velocity; Vibration
Light vector, direction of xii
Light, dispersion of 578 583 586
Light, dynamics of xii xiv 411
Light, dynamics of, correspondence on xv 583
Light, dynamics of, researches on 576
Light, propagation of, in crystals, xii xiv 413 450
Light, propagation of, in vacuo xiv 446
Light, propagation of, rectilinearity of 569
Light, propagation of, velocity of See Velocity
Light, theory of, researches respecting vibration connected with xiv 451 578
Limits, equation of 309
Linear system of particles See also Vibration
Linear system of particles, energy of vibrating 463
Linear system of particles, equations of vibration of 452 576 600
Linear system of particles, equations of vibration of, general integral of 452 490 492 576 601 602
Linear system of particles, vibrations of xiv 451 576 600
Liouville 277
Living force 3 106.
Living force, accumulated 107 108.
Living force, equation of 107
Living force, equation of, in three-body problem 2 17 25
Living force, law of 107
Living force, law of, deduced from hodograph 289
Living force, relative 121 126 150
Lloyd 439 595
Longitude of node 208
Longitude of perihelion 208
Longitude, in elliptic orbit 208
Longitude, moon's geocentric 240
Longitude, moon's geocentric, perturbations of 243 245 248 262 263 272 274 277
Longitude, perturbation of Jupiter's 10 11
Longitude, perturbation of Saturn's 14
Lovett 160 175
Lubbock's expression for perturbation of moon's coordinates 277
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