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Routh E.J. — The advanced part of a treatise on the dynamics of a system of rigid bodies. Being part II
Routh E.J. — The advanced part of a treatise on the dynamics of a system of rigid bodies. Being part II

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Название: The advanced part of a treatise on the dynamics of a system of rigid bodies. Being part II

Автор: Routh E.J.


In each successive edition of this work the author has had to state that many additions and improvements have been made. The present is no exception to this rule. The subject of dynamics grows so rapidly and so many new extensions are continually being discovered that much of every edition has had to be rewritten. There were necessarily omissions of some of the older matter, a condensation of what remained, and a selection made from the new work. The student will see by a glance at the table of contents how many and how various are the applications of dynamics and it is not to be supposed that this list is an exhaustive one.

Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1905

Количество страниц: 503

Добавлена в каталог: 19.11.2012

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Предметный указатель
Action, least, discontinuous motions      455
Action, least, examples on this test      458
Action, least, Hamilton's generalisation into Varying Action      442
Action, least, Jacobi's test that the action is a minimum      458
Action, least, two theorems      447
Airy, G.B., form of an electric cable payed out from a ship      597
Airy, G.B., governors      105 107
Airy, G.B., numerical verification of an expansion by Fourier's rule      615
Approximations, second, change of type and period      356
Approximations, second, examples      364
Approximations, second, general theory      360
Approximations, second, what terms rise in order      355
Ball, Sir R., theorems on the oscillations of a suspended body      133 214
Bernoulli, D., motion of a chain suspended by one end      599
Bernoulli, D., transference of oscillations      94
Bertrand, relative motion      25
Bertrand, remarks on a theorem of Poisson      495 497
Bertrand, theorem on (u, v)      498
Billiards, final rectilinear motion      Ex. 2
Billiards, impact of two balls      Ex. 3
Billiards, path of the centre      Ex. 1
Billiards, some numerical results      239
Billiards, various results      Ex. 4
Biquadratic, analysis for dynamics      285
Biquadratic, conditions of stability      287
Boole, proof of Lagrange's variation formula      478
Boomerang, described with general theory      210
Boomerang, G.T., Walker's memoir on the motion      210
Booth, arc of herpolhode      171 Ex.
Bour, Ed., reduction of the number of variables in theoretical dynamics, referred to      512
Bour, Ed., relative vis viva      42
Bourget, oscillations of tight connected strings      621
Bryan, G.H., a graphic illustration      467 Ex.
Bryan, G.H., report on Thermodynamics      461
Canonical elements, defined      489 491
Canonical elements, the constants in Jacobi's complete integral form a canonical set      496
Centrifugal force, compound c.f.      26
Centrifugal force, the centrifugal forces E      112 311 389
Chandler, S.C., motion of the pole in the earth      534
Changing bodies, equations of motion      22
Changing bodies, Liouville J., Darwin, Kelvin, Tisserand, Gylden, Helmert      24
Chree, C., motion of a tight string, effect of a sensible thickness      612
Clairaut, relative motion      25
Cone rolls on a moving sphere      209
Conjugate functions, applied to a heterogeneous membrane      642
Conjugate functions, applied to a network      421
Conjugate functions, theory explained      459 641
Conjugate functions, vortex motion      475
Conjugate line, defined      174
Conjugate line, theorems on its motion      175
Contact transformation, generalised Matthieu's rule      500
Coriolis, billiards      239
Coriolis, relative motion      25
Coriolis, vis viva with moving axes      30
Cournot, motion of a body on a plane quoted      240 249
Cube, oscillates on the summit of a sphere      252 Ex.
Cyclical motions, Szily's theorem      462 Ex.
Cyclical motions, the fundamental theorems      461
Cyclical motions, various references      461
Cylinder, steady motion with its edge on a plane, and the oscillations      244 Ex.
Darboux, elimination of the time in Lagrange's equations      451
Darboux, on an equation of Poisson      599
Darboux, theorem on what intersections of quadrics could be polhodes      150 Ex.
Darwin, changing body      22
Darwin, effect of geological changes on the earth's axis of rotation      540
Day, other causes      539 540
Day, the length is not affected by the attraction of the sun      539
De Morgan, discontinuity in the arbitrary functions      615
De Morgan, exceptional cases in the theory of maxima      455
Differential equations, many degrees of freedom      262
Differential equations, minors zero      272 see
Differential equations, Sturm's theorem on differential equations of the second order      427
Differential equations, the complementary function      325
Differential equations, the string differential equation      587
Differential equations, two degrees of freedom      260
Differential equations, types of motion      264
Disc or hoop, a disc spun about a diameter      244 Ex.
Disc or hoop, general equations      244
Disc or hoop, horizontal ring rotating on the summit of a sphere      208
Disc or hoop, rolls with plane vertical      15 244
Disc or hoop, steady motion and oscillations      244 Ex.
Discontinuity, discontinuous agitating force      413
Discontinuity, discontinuous motions      455
Discontinuity, the arbitrary functions in the theory of sound may be discontinuous      615
Dixon, A.C., memoir on a Theorem of Jacobi      201
Donkin, normal transformation      482
Donkin, proof that $dp_{r}/da_{s}=db_{s}/dq_{r}$      489
Donkin, reduction in the number of variables      512
Donkin, rule for transformation of coordinates in Hamilton's equations      500
Donkin, string with attached mass      622 Ex.
Donkin, string with periodic force and piano string      619 620
Donkin, the constants in Jacobi's integral form a canonical set      496
Donkin, theorem on reciprocal functions      487
Drift of shot, general explanation      210
Electric cable, effect of friction      598
Electric cable, form of, when payed out from a ship      597
Ellery, Huygliens' parabolic pendulum, referred to      107
Ellipsoid, axis vertical oscillates on a plane      252 Ex.
Ellipsoid, conjugate Ellipsoid      174 183 Ex.
Ellipsoid, motion of a contracting ellipsoid centre fixed      24 Ex.
Ellipsoid, roots of discriminant      63
Ellipsoid, two intersect in a polhode      150 175
Energy of oscillation, effects of an increase of inertia      76
Energy of oscillation, effects of an increase of inertia, and introduction of a constraint      78
Energy of oscillation, energy of a tight oscillating string      627
Energy of oscillation, intensity of a wave      627
Energy of oscillation, mean kinetic and potential      72
Energy, steady motion      99
Energy, test of stability      96
Energy, the determinant      99
Energy, the determinant, with examples      102
Euler, J.A., path of a billiard ball      239
Euler, L., complementary functions in precession      532
Euler, L., how changed if A, B, C were unequal      540
Euler, L., the ten-monthly period      533
Evans, Sir John, experiments on bodies which spin in one direction only      253
Ewing, speed governor      107
Ferrers, geometrical construction for the angular velocity in space of the instantaneous axis      169
Ferrers, on Sylvester's top      149
Ferrers, solution of a Tripos Problem quoted      130
Finite differences, applications to particles, rods, discs      418
Finite differences, chain of gyrostats, rods      419
Finite differences, chain of particles      402
Finite differences, four propositions      430 440
Finite differences, network      420
Finite differences, Sturm's theorems      433
Finite differences, theory of equations of Differences      422
Finite differences, two kinds of motion      411
Forced oscillations, Herschel's theorem      334
Forced oscillations, illustrations      340
Forced oscillations, infinite string      618
Forced oscillations, interval between cause and effect      352
Forced oscillations, magnification      337 346
Fourier, his use of the series for $J_{0}$      599
Fourier, the rule for expansion in series      398
Free oscillations, general form of the fundamental determinant      310
Free oscillations, gradual disappearance of free oscillations      321 331
Free oscillations, imaginary roots      319
Free oscillations, the three potentials      309 311
Free oscillations, theorem on real roots      315
Frost, P., his Solid Geometry quoted      199
Frost, P., moving axes      5
Gallop, a rolling disc      244
Gallop, on the rise of a spinning top      243
Gascheau, referred to      109
Geometry of moving axes, applications to the theory of curves and surfaces      21
Geometry of moving axes, condition that a line OM is fixed in space      15
Geometry of moving axes, motion of OM in space      19
Gilbert, relative motion      42 44 Ex.
Gray and Mathews, Treatise on Bessel functions      600 600
Greenhill, drift of Shot      210
Greenhill, elliptic functions quoted      203
Greenhill, geometrical representation of the time of a small oscillation of a top      205
Greenhill, gyrostat      44 Ex.
Greenhill, integrable cases of a top motion      207
Greenhill, memoirs on the motion of a top      201 201
Greenhill, oscillation of a heterogeneous chain      600 Ex.
Greenhill, problem on vortex motion      476
Greenhill, solution of Euler's equations      137
Gylden, changing body      22
Gyrostat, a general case      45
Gyrostat, application of Lagrange's equations      44
Gyrostat, chain of gyrostats      419
Gyrostat, effect of rotation of the earth      43
Gyrostat, some examples on suspended and other gyrostats      10 15
Gyrostat, various examples      46 205
Hamilton, Sir W.R., applied to the solution of the general equations of motion      463
Hamilton, Sir W.R., examples      477
Hamilton, Sir W.R., examples on the principal and characteristic functions      467
Hamilton, Sir W.R., principle of varying action      442
Hamilton, Sir W.R., some general cases in which these can be integrated      476
Hamilton, Sir W.R., the differential equations which these functions must satisfy      468
Hayward, R.B., equations of moving axes      5
Helmert, changing body      24
Helmholtz, motion of a plucked string      614 614
Helmholtz, pianoforte string      620
Helmholtz, practical analysis of a sound      340
Helmholtz, reciprocal Theorem in dynamics $\delta q_{s}/\delta a_{r}=\Delta b_{r}/\Delta p_{s}$      492
Helmholtz, the relation of Fourier's series to the human ear      615
Hemming, G.W., treatise on Billiards quoted      239
Herpolhode, cone of herpolhode      159
Herpolhode, geometrical properties of the herpolhode      470
Herpolhode, Poinsot's definition      151
Herpolhode, when $G^{2}=BT$      191
Herschel, theorem on forced vibrations      334
Hess, his integral for the motion of some tops      212
Hess, reduction      212
Huyghens, his parabolic pendulum explained      106
Impulses on a loose string      583
Impulses on a membrane      640
Impulses on a tight string      620
Impulses, impact of rods      626
Impulses, jerks in machinery      349
Impulses, no forces      146
Impulses, steady motion disturbed      118
Impulses, top      209
Indeterminate multipliers, applied to Hamilton's equations      502
Indeterminate multipliers, oscillations about equilibrium      48
Initial motions, loose string      589
Instantaneous axis, Poinsot's theorem on its motion in space      168
Instantaneous axis, the cone      159
Invariable line      141
Invariable line, the invariable cone      159
Invariable line, velocity in its sphero-conic      164 165
Inversion, deduced from the principle of least action with examples      459
Inversion, relations between the pressures      459
Isolation, method of, determinant to find the constants of integration separately      366
Isolation, method of, repeated roots      369
Jacobi, rule for transformation of coordinates      490
Jacobi, solution of Euler's equations      137
Jacobi, test that the "action" is a real minimum      458
Jacobi, the complete integral of Hamilton's differential equation      470
Jacobi, theorem on (u, v)      498
Jellett, approximate solution of a top problem      243
Jullien, referred to      109
Kater, test that a support is firm      342
Kelvin, Lord, chain of gyrostats      419
Kelvin, Lord, changing body      22
Kelvin, Lord, motion of a body about a centre of force      557 Ex.
Kirchhoff, solution of Euler's equations      139
Klein and Sommerfeld, motion of a top      201
Klein and Sommerfeld, on Hess' integral      212
Koenigs, theorem on polhodes      150 Ex.
Korteweg, D.J., on second approximations      355
Kowalevski, her integral for the motion of some tops      213
Lagrange's equations, bordered determinant      64
Lagrange's equations, change of the independent variable t (two proofs)      458
Lagrange's equations, elimination of the time from Lagrange's equations      458
Lagrange's equations, energy      72
Lagrange's equations, equal roots      61
Lagrange's equations, indeterminate multipliers      48
Lagrange's equations, invariants      68
Lagrange's equations, principal oscillations      53
Lagrange's equations, separation of roots of the determinant      58
Lagrange, a tight chain of particles      402
Lagrange, general transformation from Cartesian to other coordinates      460
Lagrange, motion of a top      200
Lagrange, small oscillations of a suspended body      214
Lagrange, stability of three mutually attracting particles      108
Lagrange, the variation formula      478
Lagrange, the variation formula, extension      479
Lagrange, the variation formula, variation of parameters      509
Lamb, H. Encyc. Brit. "Dynamics" quoted      205 Ex.
Lamb, H., reciprocal theorems in dynamics      492
Lane-Fox, remarks on the Boomerang      210
Langley, S.P., experiments on a disc falling in air      210
Larmor, J., inversion of dynamical problems      459
Larmor, J., on Least action when applied to the modified Lagrangian function      450
Latitude, variation of, Albrecht and Forster's observations      535
Latitude, variation of, Chandler's observations and Newcomb's Theory      534
Latitude, variation of, maps of the path of the pole      535
Latitude, variation of, Turner      535
Lecornu, L., the impossible motions of a rod      255
Legendre, motion when $G^{2}=BT$ referred to      184
Levi-Civita, on stationary motion      213
Liouville, J., changing body      22
Liouville, J., moving axes      5
Liouville, R., his discussion of Hess' integral      212
Lottner, relative motion      42 46 Ex.
MacCullagh, construction for a body under no forces      152
MacCullagh, geometrical interpretation      515
MacCullagh, geometrical solution of Euler's equations      153
MacCullagh, potential of a body at a distant point      513
Mackinlay, text book of Gunnery quoted      210
Magnus, deviation of projectiles quoted      210
Maxwell, essay on Saturn's rings      557 Ex.
Maxwell, on Governors      107
Membrane, equation in a series to find the load to produce a given period      639 639 474
Membrane, heterogeneous membranes      641
Membrane, vibrations due to a periodic force, or a blow      640
Membrane, vibrations when bounded by a rectangle      635
Moon, two important constants      556
Moscow collections, memoirs on Hess' integral      212
Moving axes, equations of motion and examples      10
Moving axes, fundamental theorem      4
Moving axes, fundamental theorem, oblique axes      7
Moving axes, fundamental theorem, vectors      5
Moving axes, geometry of      16
Moving axes, rolling hoop      15
Moving axes, small oscillations      15
Moving axes, top, axis vertical      15
Moving axes, uniaxal bodies      12
Multipliers, method of, equal roots      392
Multipliers, method of, extension to other cases in dynamics (1) symmetrical determinant      384 386
Multipliers, method of, extension to other cases in dynamics (2) skewed determinant      389
Multipliers, method of, Fourier's rule      398
Network of particles, conjugate functions      421
Network of particles, quadrilateral openings      420
No forces, conjugate line      174
No forces, Correlated bodies      192
No forces, MacCullagh      152
No forces, motion of principal axes      176
No forces, motion under      137
No forces, Poinsot      143
No forces, resistance of the air      147
No forces, sphero-conics      161
No forces, Stone's theorem      183 Ex.
No forces, sudden action of forces      146
No forces, Sylvester's and Poinsot's measures of the time      196 198
No forces, uniaxal bodies      180
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