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Routh E.J. — A treatise on dynamics of a particle
Routh E.J. — A treatise on dynamics of a particle

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Название: A treatise on dynamics of a particle

Автор: Routh E.J.


So many questions which necessarily excite our interest and curiosity are discussed in the dynamics of a particle that this subject has always been a favourite one with students. How, for example, is it that by observing the motion of a pendulum we can tell the time of the rotation of the earth, or knowing this, how is it that we can deduce the latitude of the place? Why does our earth travel round the sun in an ellipse and what would be the path if the law of gravitation were different? Would any other law give a closed orbit so that our planet might (if undisturbed) repeat the same path continually? Is there a resisting medium which is slowly but continually bringing our orbit nearer to the sun? What would be the path of a particle in a system of two centres of force? When a comet passes close to a planet does it carry with it in its new orbit some tokens to prove its identity?

Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1898

Количество страниц: 435

Добавлена в каталог: 15.10.2012

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Предметный указатель
Accelerating force      68
Acceleration, Components in three dimensions      490 &c.
Acceleration, Components in three dimensions, Moving axes      498
Acceleration, Components in two dimensions      38
Acceleration, Components in two dimensions, Moving axes      223
Acceleration, Hyper acceleration      233
Adams, J, C, Motion of a heavy projectile      178
Adams, J, C, Proof of Lambert’s theorem      352
Adams, J, C, Resistance to comets      386
Adams, J, C, The true and mean anomalies      347
Algol, Two problems      405
Allegret, Problem on the resistance to a projectile      176 Ex. 4
Ambiguous signs, In Euler’s and Lambert’s theorems in elliptic motion      350 353
Ambiguous signs, In rectilinear motion &c      97 100
Anomaly, Defined      342
Anomaly, Various theorems      346
Apse, Apsidal angle and distances found      367 422
Apse, Apsidal angle and distances found, when independent of the distance      368 370
Apse, Apsidal boundaries      441
Apse, Conditions there are two, one, or no apsidal distances      430-433
Apse, Conical pendulum      564
Apse, Defined, apocentre and pericentre      314
Apse, Equal apsidal distances      434
Apse, Equal apsidal distances, apsidal circle      434 436
Apse, Second approximations      370 426 427
Asymptotic circles, In central orbits      434 446
Atwood, Machine      60
Backlund, Resistance to Encke’s comet      385 note.
Ball, History of mathematics      591 note.
Barrier curves, Boundaries of the field      299
Barrier curves, In brachistochrones and least action      649
Bashforth, Law of resistance      171
Bashforth, Motion of projectiles      169
Bertrand, Brachistochrones      610
Bertrand, Closed orbits      428
Bertrand, General and particular integrals      245
Bertrand, Law of gravitation      393 Ex. 2 3
Bertrand, The apsidal angle      426
Besant, On infinitesimal impulses      148 note.
Bonnet, Superposition of motions      273
Brachistochrones, A conic      605 Ex. 1 606 6
Brachistochrones, A cycloid      601 &c.
Brachistochrones, Case in which the construction fails      649
Brachistochrones, Central force      606
Brachistochrones, In space      591
Brachistochrones, In space, on a cone, cylinder, &c      612
Brachistochrones, In space, on a surface      607
Brachistochrones, Relation to the free path      598 599 606
Brachistochrones, Vertical force      601
Bryant, True and mean anomalies      347 Ex. 5
Burnside and Panton, quoted      489 note.
Callandreau, Encke’s comet      385
Callandreau, On Tisserand’s criterion      415
Callandreau, Spherical swarm      414
Callandreau, The disintegration of comets, page      407
Cardioid, A central orbit      320
Catenary, A brachistochrone      606 Ex. 7
Catenary, A tautochrone      211
Cauchy, Convergency of the series in Kepler’s problem      488
Cayley, Elliptic functions      218 220 364
Cayley, Infinitesimal impulses      150 Ex. 3
Cayley, Lambert’s theorem      352 note.
Cayley, Motion in an ellipse with two centres of force      355 Ex. 4
Central force, Cotes’ spirals      356
Central force, Elementary theorems, &c      306
Central force, Force $=\mu u^{n}$, classification of the orbits      436
Central force, Inverse fourth, fifth, &c      364 365
Central force, Locus of centres for a given orbit      421
Central force, Solution by Jacobi’s method in three dimensions      645
Central force, Solution when the velocity is that from infinity      360
Central force, Solution when the velocity is that from infinity, disturbed path      363 Ex. 8
Central force, Solution when the velocity is that from infinity, time      362
Central force, Stability      439
Central force, The inverse cube, rectilinear motion      100
Central force, The inverse cube, rectilinear motion, lemniscate      190 Ex. 11
Centrifugal force, Explained      183
Challis, Infinitesimal impulses quoted      148 note.
Chords of quickest descent, Smooth and rough      143 &c.
Circle, A rough circle      192
Circle, A rough circle, a moving circle      198
Circle, Central force      318 321 190
Circle, coaxial circles      219
Circle, Continuous and oscillatory      216
Circle, Geodesic circles      548 571
Circle, Motion of a heavy particle, time just all round      201 Ex. 1
Circle, Nearly circular orbits      367
Circle, Nearly circular orbits, least action      653
Circle, Nearly circular orbits, second approximation      369 370
Circle, Parallel force $Y=\mu/y^{3}$      323 452
Circle, Time in any arc      213
Circle, Two centres of force      194
Circle, When the force is infinite      466
Classification      460
Clerke, History of Astronomy quoted      385 note.
Conic, A brachistochrone      606 Ex. 3 4
Conic, A corresponding curve on an ellipsoid      572
Conic, AS a central orbit with any centre, there are two laws of force      456
Conic, Elements of the conic      457
Conic, Time      454
Conical Pendulum, Apsidal angle      564
Conical Pendulum, Projection a central orbit      560
Conical Pendulum, Radius of curvature      559
Conical Pendulum, Rise and fall      558
Conical Pendulum, Tension      557
Conical Pendulum, The cubic      555
Conical Pendulum, Time of passage      562
Conjugate functions, Relation between the motions      633
Conjugate functions, Relation between the pressures      635
Conservative system, Explained      181
Conservative system, Forces which disappear in the work function      248
Conservative system, Oscillations      294
Constant of gravity      66
Convergency, The series in Kepler’s problem      488 &c.
Coriolis, Theorem on relative vis viva      257
Craig, Particle on an ellipsoid      568
Craig, Treatise on projections referred to      609
Curve, Motion in two dimensions, fixed      181
Curve, Motion in two dimensions, moving      197
Curve, Motion in two dimensions, rough      191
Curve, Three dimensions, changing      533
Curve, Three dimensions, fixed      526
Curve, Three dimensions, moving      528
Cycloid, A brachistochrone      601 602
Cycloid, A brachistochrone, theorems      603 &c.
Cycloid, A tautochrone      204
Cycloid, A tautochrone, rough      212
Cycloid, A tautochrone, theorems      206
Cycloid, Resisting medium      210
Cylinders, Brachistochrones      612 Ex. 3
Cylinders, Motion on      544
Darboux, Elimination of the time in Lagrange’s equations, page      410
Darboux, Force in a conic      450
Darboux, Relation of brachistochrones to geodesics      609
Darboux, The apsidal angle      427
Darwin, Periodic orbits      418 note.
Darwin, Swarm of meteorites, page      407
Degrees of freedom, defined      252
Despeyrons, Problem on time in an arc      203 Ex. 1
Dimensions, General theory      151
Dimensions, In central orbits      316
Direct distance, Central force, &c      325
Direct distance, Time in an arc of lemniscate      201 Ex. 2 3
Direct distance, With this law of force, rectilinear motion with friction      125
Direct distance, With this law of force, rectilinear motion with friction, and resistance      126
Discontinuity, Of a central force      135
Discontinuity, Of brachistochrones      604 649
Discontinuity, Of orbits      467 &c.
Discontinuity, Of resistance      128
Discountinuity, Of friction      125 191
Double answers, In rectilinear motion      98
Double answers, In two dimensions      266
D’Alembert, The principle      236
Effective force, Defined      68 235
Effective force, Resultant effective force and couple      239
Effective force, Virtual moment      507
Ellipsoid, Cartesian coordinates      568
Ellipsoid, Cartesian coordinates, a case of integration      569 575
Ellipsoid, Central force      570 571 572
Ellipsoid, Elliptic coordinates      576
Ellipsoid, Elliptic coordinates, a case of integration      578 582
Ellipsoid, Motion on a line of curvature      583
Ellipsoid, Spheroidal coordinates      584
Elliptic coordinates, Three dimensions      576
Elliptic coordinates, Translation into Cartesian      576 580
Elliptic coordinates, Two dimensions      585
Elliptic motion, Bessel      480
Elliptic motion, Change of eccentricity and apse, &c. by a resisting medium      383
Elliptic motion, Change of eccentricity and apse, &c. by forces      380
Elliptic motion, Disturbed by continuous forces      376
Elliptic motion, Disturbed by impulses      371 &c.
Elliptic motion, Elliptic velocity      397
Elliptic motion, Kepler’s problem      473
Elliptic motion, Lagrange      479
Elliptic motion, Time found      342 345
Encke, Resistance to a comet      385
Energy, In central forces      313; see also vis viva.
Energy, Principle of      250
Epicycloid, A central orbit      322
Epicycloid, A tautochrone      211
Epicycloid, Force infinite      472 Ex. 2
Equiangular spiral, A central orbit      319
Equiangular spiral, A central orbit, particle at centre of force      470
Equiangular spiral, A tautochrone      211
Equiangular spiral, Moving spiral      198 Ex. 2
Equiangular spiral, Pressure      190 Ex. 8
Euler, Brachistochrones with a central force      591 note.
Euler, Lemniscate      201 Ex. 2
Euler, On motion in a parabola      350
Euler, Problem on a rebounding particle      305 Ex. 4
Euler, With two centres of force      585 note.
Finite diffreences, Problems requiring      305
Foesyth, Differential equations      243
Foesyth, Theory of functions      489
Foucault, Pendulum referred to      57 627
Foucault, Theory      624 626
Friction, Discontinuity      125 191
Friction, Rough chords with gravity      104
Friction, Rough chords with gravity, centre of force      133
Friction, Rough curve      191
Frost, Elliptic velocity      397
Frost, Singular points in a circular orbit      466
Gauss, Coordinates      546 547
Geodesic, Brachistochrones Bertrand      610
Geodesic, Circles on ellipsoid      548
Geodesic, Darboux      609
Geodesic, line      539
Geodesic, Roberts      571
Glaisher, Force in a conic      450 note.
Glaisher, Time in an ellipse      347 Ex. 1 476
Gray and Mathews, Kepler’s problem      481
Gray and Mathews, Treatise on Bessel functions      286 Ex. 9
Greenhill, An integral      116
Greenhill, Conical pendulum      555 note.
Greenhill, Cubic law of resistance      177
Greenhill, Elliptic functions      213 note 364
Greenhill, Motion of projectiles      169
Greenhill, Paths for a central force $\mu u^{n}$, special values of $n$      356 note.
Greenhill, Stability of orbits and asymptotic circles      429 note
Grouping, Of trajectories of a particle, Theory      636 638
Grouping, Special cases      159 330 339
Guglielmini, Experiments on falling bodies      627
H$\acute{e}$li$\k{c}$oide, Motion on, another problem      543 Ex. 5
H$\acute{e}$li$\k{c}$oide, Motion on, Liouville’s solution      583 Ex. 4
Haerdtl, Traces path of a planet in a binary system      418 Ex. 2
Hall Maxwell, On Algol      405 Ex. 1
Hall, Asaph, Satellites and mass of Mars      403
Hall, Asaph, Singular points in central orbits      465 note.
Halphan, Force in a conic      450 note.
Halphan, Law of gravitation      393 Ex. 1
Hamilton, Hamiltonian equation      640
Hamilton, Hodograph      394
Hamilton, Law of force in a conic      453
Harmonic oscillation, Definition, frequency, amplitude, &c      119
Helix, Heavy particle on, fixed      527
Helix, Heavy particle on, moving      534
Herschel, Algol      405
Herschel, Disturbed elliptic motion      379
Hill, Stability of the moon’s orbit      417
Hodograph, Central orbits      394
Hodograph, Elementary theorems      29
Hodograph, Itself a central orbit      398
Hopkins, Infinitesimal impulses      148 note.
Horse-power, Defined      72
Huygens, Terminal velocity      111
Impulses, How measured      80
Impulses, Infinitesimal      148
Impulses, Smooth bodies      83 &c.
Inertia, Explained      52 183
Inertia, moment of      241
Infinite, Force      100 466
Infinite, Subject of integration infinite      99 202
Ingall, Motion of projectiles quoted      169
Initial, Initial motion deduce from Lagrange’s equations      517
Initial, Starting from rest      280
Initial, String of particles      279
Initial, Tension and curvature      276 &c.
Initial, Three attracting particles fall from rest      284 Ex. 6
Integrals, A general case in three dimensions      497
Integrals, A general case in three dimensions, in Jacobi’s method      645
Integrals, General and Particular integrals      244 245
Integrals, Integrals of Lagrange’s equations      521 and page 408
Integrals, Liouville’s      522
Integrals, Of the equations of motion, Two elementary      74 75
Integrals, Rectilinear motion      97 101
Integrals, Summary of methods in two dimensions      264
Inverse square, law of, Central force      332 &c; see Time.
Inverse square, law of, Particle falls from a planet      134
Inverse square, law of, Rectilinear motion      130
Inversion, Calculus of variations      650 Ex. 2
Inversion, Of the impressed forces      631 632
Inversion, Of the motion of a particle      628
Inversion, Of the pressure on a curve, &c      631
Jacobi, Case of solution of Lagrange’s equations      523
Jacobi, Criterion of max-min in the calculus of variations      594 648
Jacobi, Integral for a planet in a binary system      255 415 417
Jacobi, Method of solving dynamical problems      640 644
Jacobi, Two centres of force      585 note.
Jellett, On brachistochrones      591 note 650
Kepler, Kepler’s problem      473
Kepler, Law of gravitation in the solar and stellar systems      390
Kepler, The laws      387
Korteweg, Stability, asymptotic circles, &c      429 note.
Lachlan, Treatise on modern geometry referred to      219
Lagrange, Conical pendulum      555 note.
Lagrange, Energy test of stability      296
Lagrange, Two centres of force      585 note.
Lagrange’s equations, Change of the independent variable      524 and page 408
Lagrange’s equations, Elementary resolutions deduced      512 Ex. 1 2
Lagrange’s equations, Elementary resolutions deduced, vis viva deduced, Ex      3
Lagrange’s equations, Elimination of the time, page      409
Lagrange’s equations, Initial motion      517
Lagrange’s equations, Methods of solution      521 and page 408
Lagrange’s equations, Proof      503 &c.
Lagrange’s equations, Small oscillations      513
Lagrange’s equations, Transference of a factor      524
Laisant, On a case of vis viva      258
Lam$\acute{e}$, On curvilinear coordinates      525
Lambert, Time in an elliptic arc      352
Laplace, Convergency      488
Laplace, On three attracting particles      406
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