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| Hamilton W.R. — The collected mathematical papers. Volume 2: dynamics |
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| Предметный указатель |
Principal relations, calculus of xi xiv 105 163 212 297 332 334 358 408
Principal relations, for differential expression of first order xi 332
Principal relations, for system of differential equations of any order xi 360 372
Principal relations, for system of differential equations of first order 368
Principal relations, for system of differential equations of second order 372
Principal relations, for total differential equation of first order xi 297 316 358 364 408
Principal relations, fundamental theorem of 363 364
Principal relations, particular cases 375
Principal supplementary equations of differential expression of first order 333
Principal supplementary equations of system of differential equations of any order 360 362 372 373 374
Principal supplementary equations of system of differential equations of first order 368 370
Principal supplementary equations of system of differential equations of second order 372
Principal supplementary equations of total differential equation of first order 302 303 316 358 364 408
Principal value, Cauchy's 469 516 552 580
Principia 100 286
Principle of equivalent vibrations 437
Principle of fluctuation 520 581
Principle, Hamilton's 167
Principle, Rayleigh's xii 340
Principles of least, stationary and varying action See Action
Prismatic dispersion 594
Prismatic spectra 594
Problem of perturbation 171 177
Problem of three bodies See Ternary system; Three-body problem
Problem of two bodies See Binary system; Elliptic motion; Planetary motion
Problem, capital, of dynamics 212
Problems of perturbation, calculus of principal relations applied to 250 257 278
Progress of wave, velocity of 577. See also Group-velocity; Velocity of propagation of vibration
Progressive wave, simple See Travelling sinusoid
Projectile, integrals of motion for 186 187 188
Projectile, motion of 186
Projectile, motion of, disturbing function for 189
Projectile, motion of, function of elements for 193 196
Projectile, motion of, Hamilton's equations for 186
Projectile, motion of, perturbations of 188
Projectile, motion of, principal function for 186 187
Projectile, motion of, principal function for, approximations to 189 190 191
Projectile, motion of, principal function for, disturbing part of 189 190 191
Projectile, motion of, varying elements for 192
Projectile, motion of, with variation of gravity 197
Propagation of disturbance, velocity of 606
Propagation of light in crystals xii xiv 413 450
Propagation of light in vacuo xiv 446
Propagation of light, rectilinearity of 569
Propagation of motion in elastic medium 527
Propagation of plane wave in crystal, velocities of 423 427 433
Propagation of vibration 413 450 451 527 576 578 599
Propagation of vibration, general law of 571 572
Propagation, slowness of 417 596
Propagation, velocity of 510 517 556 560 571 572 574 575 582 605.
Propagation, wave-, Fresnel's law of, in biaxal crystal 433 434 444 639
Propagation, wave-, Fresnel's law of, in dispersive crystal 438 439 444 445 639
Propagation, wave-, law of velocity of, in dispersive medium 447 582 584 586 596
Q function 167 170
Q function, integrals of motion deduced from 167
Q function, law of variation of 167
Q function, partial differential equations for 169
Q function, relation of principal function to 168
Quantity of vibration 463
Quaternions 286 287 291 293
Radius vector, centrobaric, perturbations of 57 67
Radius vector, heliocentric, perturbations of 71
Radius vector, Jupiter's, perturbations of 9 10 11
Radius vector, Moon's geocentric, perturbations of 243 245 248 262 263 272 274 277
Radius vector, Saturn's, perturbations of 14
Rayleigh xii 340 490
Rayleigh's principle xii 340
Reciprocal hodographs 288
Reciprocal theorem in dynamics xv 451 458 490
Rectilinearity of light propagation 569
Reflection and refraction of light in crystals 435
Reflection and refraction, laws of 437
Reflection of vibrations 457 459
Refraction See also Reflection and refraction
Refraction, astronomical 98
Refraction, atmospheric 96
Refraction, indices of, effect of heat on 440
Refraction, indices of, in Iceland Spar 439 440
Relation between five points in space 146
Relations, calculus of principal See Principal relations
Relative action See Action
Relative coordinates 113 198
Relative coordinates for binary system 207
Relative hodograph 290
Relative living force 121 126 150
Relative motion 121 197
Relative motion, characteristic function for 121
Relative motion, characteristic function for, in binary system 134
Relative motion, characteristic function for, in elliptic orbit 136
Relative motion, characteristic function for, in ternary system 143 147
Relative motion, characteristic function for, variation of 121
Relative motion, principal function for 200
Relative motion, principal function for, variation of 200
Relative orbit, plane 135 136
Relative position, marks of 125
Resisting medium, approximation to principal function for motion in 351
Riccati 563
Rings, phenomena of 445
Ritdberg 439
Ritz 340
Routh 168 206
S function See Principal function
Salmon 146
Saturn's longitude, perturbations of 14
Saturn's radius vector, perturbations of 14
Saturn, equations of motion of 2
Saturn, perturbations of 12
Saturn, perturbations of, in centrobaric coordinates 20
Saturn, perturbations of, in heliocentric coordinates 70
Semi-infinite linear system of particles, vibration of See Infinite linear system
Sinusoid 488 489 492
Sinusoid, fixed 502
Sinusoid, oscillating 497
Sinusoid, travelling 497 499 501 502
Sinusoidal mode of vibration 488 489 492 495 497
Sinusoidal wave 451
Skotodynamics xii. See also Darkness dynamics
Slowness of propagation of wave 417
Slowness, vector of 293
Solar system, approximation to characteristic function for 83 94
Solution, common, of partial differential equations for 7 79
Sommerfeld 571
Spectra, prismatic 594
Spectrum of interference 591
Spectrum, diffraction 591
Sphero-conic, description of, under central force xiii 286
Square system of particles, vibration of 568
Squares, method of least 594
Star, aberration of 290
Stationary action, law of See Action
Strained cubic lattice 418 450
Sun, central 291 292
Supplementary equations, principal See Principal supplementary equations
Surface, wave-, double, in Iceland Spar 441
Surface, wave-, Fresnel's 432 442
Surface, wave-, in dispersive crystal 444
System of total differential equations See also Binary; Linear; Multiple; Solar; Square; Ternary
System of total differential equations, calculus of principal relations applied to See Principal relations
System of total differential equations, principal integral of See Principal integral
Systems of bays, theory of 105 214
T function See Living force; Vis viva
Tables, lunar 249 256
Tait 106
Taylor 335 354
Taylor's theorem 335 354
Ternary system 140. See also Lunar theory; Moon theory
Ternary system, characteristic function for 140
Ternary system, characteristic function for, disturbing part of 154
Ternary system, characteristic function for, law of variation of 143
Ternary system, force-function for 140
| Ternary system, integrals of motion of 142 143 144
Ternary system, law of varying action for 142
Ternary system, partial differential equations for V 142 143
Ternary system, variational equation for 140
Ternary system, with one predominant mass, perturbations of 150 200
Theorem See Euler's; Fourier's; Hamilton's; Lambert's; Reciprocal; Taylor's
Theorem, fundamental, of calculus of principal relations 363 364
Theorem, fundamental, of dynamics 3
Theoretical dynamics, development of 104
Theory of light See Light theory
Theory of Moon See Lunar theory; Moon theory
Theory of Systems of Rays 105 214
Thickness of wave 417 421
Thin plates, phenomena of 597
Three bodies, problem of See Three-body problem
Three-body problem x xii 1 230. theory
Three-body problem, application of characteristic function to xii 1
Three-body problem, characteristic function for 3
Three-body problem, characteristic function for, approximation to 25 27 32 44 53
Three-body problem, characteristic function for, variation of 3
Three-body problem, disturbing function for 32 34 44 49 53 231 232
Three-body problem, disturbing function for, approximation to 49 237
Three-body problem, disturbing function for, Hamilton's and Laplace's compared 51
Three-body problem, disturbing function for, heliocentric 70
Three-body problem, disturbing function for, variation of 37
Three-body problem, elements in, approximate determination of 14
Three-body problem, elliptic elements in, perturbations of 32
Three-body problem, partial differential equations for S in 230 231 233 234
Three-body problem, partial differential equations for V in 5
Three-body problem, perturbations in 5 20 30 231 235
Three-body problem, principal function for 230
Three-body problem, principal function for, approximation to 235
Three-body problem, principal function for, variation of 233
Three-body problem, time in, approximation to 37 612
Three-body problem, vis viva in, approximation to 17
Three-dimensional waves in dispersive medium 569
Time in parabolic orbit 75 139 294
Time in planetary orbit 139 140
Time obtained from characteristic function 49 108
Time of perihelion passage 208
Time, approximation to, in multiple system 155 156
Time, approximation to, in three-body problem 37 612
Total derivatives, Lagrange's notation for 316 317 336
Total differential equations See Principal integral; Principal relations calculus
Transformation, contact 179
Transmission of phase, velocity of 459 487 491 494 496 510 517 582.
Transverse vibrations See Vibration of linear system
Travelling sinusoid 497 499 501 502
True anomaly 208
Turner 267
Two bodies, problem of See Two-body problem
Two variables, principal integral for differential expression in 344
Two variables, principal integral for differential expression in, examples of 348
Two-body problem See Binary system; Elliptic motion; Parabolic motion; Planetary motion
Two-dimensional waves in elastic medium 568
U function See Force-function
Ullswater 599
Ultimate state of vibration in elastic medium 555 565 566
Undisturbed motion of binary system 202
Undisturbed motion of general system, integrals of 171 174
Undisturbed motion of general system, principal function for 171
Undisturbed motion of multiple system, integrals of 200
Undisturbed motion of particle 183
Undisturbed motion of planet, principal function for 217 624
Undisturbed motion of projectile 188 189
University of Dublin 283
Uranus 291
V function See Action function; Characteristic function
Vacuo, propagation of light in xiv 446
Value, asymptotic xv 539 547 554
Vandermonde 523
Vandermonde's notation for factorials 523
Variation of constants, method of 175 249. method
Variation of elements, method of 174 622
Variation of gravity, projectile with 197
Variation of parameters, method of See Parameters method
Variation, law of See Action function; Characteristic function; Disturbing function; Elements function
Variational equation for binary system 128
Variational equation for ternary system 140
Variational equation in lunar theory 239 257
Variational equation, Lagrange's 105 164 212
Variations, calculus of xi 107 109 166 303 309 317 359 363 391 408
Variations, calculus of, applied to integration of partial differential equations xiv 391
Varying action See Action
Varying elements See Elements varying
Varying ellipse 208 209 269
Varying orbit 208 209 269
Vector of eccentricity 290
Vector of position 287
Vector of slowness 293
Vector of velocity 287 293
Vector, hodographic 291
Vector, light, direction of xii
Velocities, wave-, in crystal 423
Velocities, wave-, in dispersive crystal 437 439 441
Velocity of extinction 571
Velocity of light in Iceland Spar 439 441 442
Velocity of passage of phase 577 581
Velocity of progress of vibration 577
Velocity of propagation of disturbance 606
Velocity of propagation of vibration 510 517 556 560 571 572 582 605
Velocity of transmission of phase 459 487 491 494 496 510 517 582
Velocity, areal 208
Velocity, centrobaric 199
Velocity, distinction between group- and phase- xv 510 517 556 571 572 577 582 602 641
Velocity, group- xii. See also Velocity of progress of vibration; Velocity of propagation of disturbance; Velocity of propagation of vibration
Velocity, heliocentric 208
Velocity, phase- xii 451 556 605.
Velocity, vector of 287 293
Velocity, wave-, Fresnel's law of, in biaxal crystal 433 434 444 639
Velocity, wave-, in aether 447 448
Velocity, wave-, law of, in dispersive medium 447 582 584 586 596
Venter 454 456
Vibrating system, energy of 463
Vibrating system, equations of motion of 413 446 569 578
Vibration in aether, propagation of 446
Vibration in crystals, propagation of 413 450
Vibration in elastic medium, equations of 527
Vibration in elastic medium, equations of, general integral of 547 548 576 601 602
Vibration in elastic medium, for large values of t 555 565 566
Vibration in elastic medium, propagation of xv 527 599
Vibration of cubic system 418
Vibration of infinite linear system 458 459 460 461 465 482 502 503 511
Vibration of infinite linear system, recapitulation of results 495
Vibration of linear system 451 576 600
Vibration of linear system, for large values of t 503
Vibration of linear system, initially oscillating in simple mode 463
Vibration of linear system, initially oscillating in simple mode, progressive wave 487 497
Vibration of linear system, one particle vibrating in prescribed manner 511
Vibration of linear system, passage from finite to infinite system 465 468 477 495 500
Vibration of linear system, passage from infinite to finite system 478 482 485
Vibration of linear system, permanent mode of 489 492 495 496 498 499
Vibration of linear system, recapitulation of results 488
Vibration of linear system, with arbitrary initial conditions 451 576
Vibration of semi-infinite linear system 457 459 460 461 465 482 500 511
Vibration of semi-infinite linear system, recapitulation of results 492
Vibration of square system 568
Vibration, directions of, in crystal 423
Vibration, general law of propagation of 571 572
Vibration, quantity of 463
Vibration, researches respecting, connected with theory of light xiv 451 578
Vibration, sinusoidal mode of 488 489 492 495 497
Vibration, velocity of progress of 577
Vibration, velocity of propagation of 510 517 556 560 571 572 582 605
Vibrations in crystals, law of vis viva for 437
Vibrations, principle of equivalent 437
Vibrations, reflection of 457 459
Vis viva 106 See
Vis viva, approximations to, in three-body problem 17
Vis viva, derivative of V with respect to x xii 46 49 108
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