Routh E.J. — A treatise on dynamics of a particle :: Электронная библиотека попечительского совета мехмата МГУ

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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.

Аннотация:

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?

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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

Laplace, Other expansions      487 Ex. 3 4 5
Laplace, Series for longitude of a planet, &c      476
Larmor, Calculus of variations      591 note.
Larmor, Inversion      628 note.
Laws, Of Kepler      387
Laws, Of motion      51
Laws, Of resistance      171
Least action, A minimum      647 648
Least action, Case when there is no free path      649
Least action, Parabola, ellipse and any central orbit      651
Least action, principle of      646
Least action, Relation to brachistochrones      650 &c.
Least action, Terms of the second order      653 654
Legendre, Central orbits      356 note.
Legendre, Two centres of force      585 note.
Lejeune Dirichlet, Energy test of stability      296 note.
Lemniscate, A brachistochrone      606 Ex. 5
Lemniscate, Centre of force in the node      320
Lemniscate, The pedal a central orbit      363 Ex. 2
Lemniscate, Time in an arc      201 Ex. 2 3
Lemniscate, Two centres of force, free      587 Ex. 4
Lemniscate, Two centres of force, pressure      190 Ex. 11
Leverrier, True and mean anomalies      347
Limiting velocity, Explained      111
Limiting velocity, Theorems      115 116
Linear equations, Elementary cases      122; see Oscillations.
Linear equations, Theory      118
Liouville, A particle on an ellipsoid      568 note.
Liouville, Solution by Jacobi’s method of a class of problems      645
Liouville, Solution of Lagrange’s equation      522
Liouville, The line arrangement of three attracting particles      406 note.
Liouville, Two centres of force      585 note.
Lloyd and Hadcock, Treatise on Artillery, &c      169 note.
Magnification, Central orbits      369
Magnification, In two dimensions      303
Magnification, Rectilinear motion      139
Mass, Of a planet      403
Mass, Problems on bodies without mass      267
Mass, Units      63
Maxwell, Laws of motion quoted      51
Mayevski, The law of resistance      171
Mean distance, Of a planet, Mean value of $r^{n}$       344
Miller, Comparison of standards      63
Momentum, angular      79 492
Momentum, Conservation of linear and angular      92
Momentum, Equation of moments in central forces      306
Momentum, Equation of moments in three dimensions      492
Momentum, Equation of moments in two dimensions      259
Momentum, linear      54 79
Moving axes, Geometrical relations between relative and actual path      229
Moving axes, in three dimensions      498
Moving axes, In three dimensions, deduced from Lagrange’s equations      512 Ex. 2
Moving axes, in two dimensions      223
Moving axes, Moving central orbits      359
Moving axes, Moving curves      197
Moving axes, Oblique axes      232
Muirhead, On the laws of motion, referred to      51 note.
Newton, Central forces, a circle      318
Newton, Central forces, a conic about any centre      450
Newton, Central forces, a moving orbit      359
Newton, Constant of gravity      67
Newton, Law of elasticity      83
Newton, Laws of motion      51
Newton, Two attracting spheres      134 Ex. 3
Niven, Motion of projectiles      169 note.
Orbits, A central orbit is a brachistochrone      606
Orbits, Bertrand on closed orbits      428
Orbits, Classification of orbits for      436
Orbits, Orbits at a great distance      438
Orbits, Orbits near the origin      437
Orthogonal Coordinates, Examples and Lamp’s generalization      525
Oscillations, About a steady motion      304
Oscillations, Insufficiency of a first approximation      302
Oscillations, Of a series of particles      305
Oscillations, Of suspended particles      300
Oscillations, One degree of freedom      285
Oscillations, Principal oscillations      292
Oscillations, Problems      138
Oscillations, Small curvilinear      199
Oscillations, Small finite      200
Oscillations, Small rectilinear      137
Oscillations, Two degrees of freedom      287
Oscillations, Use of Lagrange’s equations      513
Painlev $\acute{e}$ , Elimination of time from Lagrange’s equations, page      409
Painlev $\acute{e}$ , Particle on an ellipsoid      568 note.
Parallel forces, Constant      see Projectile.
Parallel forces, Variable a conic described      323 452
Parallelogram law, Vectors      222
Parallelogram law, Velocity      4
Parallelogram law, Velocity, acceleration      28
Parallelogram law, Velocity, angular velocity      43
Path, Central forces      309
Path, Laplace’s differential equation      268
Path, Solution in some cases      269 &c.
Pendulum, Change of place      207 &c; see Circle and Conical Pendulum.
Pendulum, Rotation of the earth      621 624
Point to point, A brachistochrone      591
Point to point, Least action      646
Point to point, Path under gravity      159
Point to point, Under a central force      330 339
Poisson, Effect of the rotation of the earth      627
Poisson, Expansion of true anomaly, &c      487 Ex. 3
Pressure, A constrained motion may be free      190 193 194 529
Pressure, Does the particle leave the curve      195
Pressure, Three dimensions      526 &c. 536 552 560
Pressure, Two dimensions      184
Projectiles, Deviation from parabolic motion      623
Projectiles, Given trajectory find the resistance      179
Projectiles, In vacuo      154
Projectiles, In vacuo, by Jacobi’s method      645
Projectiles, Resistance       162
Projectiles, Resistance $kv^{n}$       168
Projectiles, Resistance $kv^{n}$ ,       176 Ex. 5
Projectiles, Resistance $kv^{n}$ ,       177
Projectiles, Resistance $kv^{n}$ , cases of       172
Projectiles, Rotation of the earth, high and flat trajectories      621
Puisseux, The spirals of      322
Pulleys      78 Ex. 10
Reciprocal spiral, A central orbit $r\theta = a$       358
Reciprocal spiral, Arrival at the centre of force      472
Reciprocal spiral, Radial velocity constant      358
Reich, Experiments at Freiberg      627
Relative motion, Acceleration relative to a moving curve      197
Relative motion, Acceleration relative to a moving point      39 276
Relative motion, Coriolis      257
Relative motion, Relative and actual paths      229
Relative motion, Three dimensions, relative to a moving curve      530
Relative motion, Three dimensions, relative to the meridian plane      495

Representative particle, Defined      295
Resisting medium, Curvilinear motion of a heavy particle      162 180
Resisting medium, Heavy particle on a chord      107
Resisting medium, Heavy particle on a chord, falls freely      115 &c.
Resisting medium, Law of resistance      171
Resisting medium, Rectilinear motion, light particle      102
Resisting medium, Resistance in the solar system      385
Roberts, R, A, Integral calculus referred to      116
Roberts, W, B, W, Motion on an ellipsoid      568 571
Roger, On brachistochrones      591 note 612
Rouch $\acute{e}$ Convergence in Kepler’s problem      488
Salmon, Solid geometry referred to      577 610
Sang, Heavy particle on a circle      217
Schiaparelli, Disintegration of comets      414 note.
Second approximations, Central orbits      367 426
Second approximations, Conical Pendulum      562 564
Second approximations, Motion, curvilinear      202 302 303
Second approximations, Rectilinear motion      141
Serret, Lemniscate      201 Ex. 2
Serret, Two centres of force      585 note.
Similar, configurations      265 Ex. 9 10
Similar, Line arrangement of three particles      409 &c.
Similar, Triangle arrangement      407
Singular points, Arrival at the centre of force      468
Singular points, Of infinite force      466
Singular points, Special cases      470 472
Slesser, Acceleration for moving axes      500
Spheres, Energy lost      90
Spheres, Impacts of smooth spheres      83 &c.
Spheres, Impulses of spheres inside moving vessels, tied by strings, &c., examples      94
Spheres, Motion of a point on a sphere      542 &c. 555
Stability, Energy test      296
Stability, Of central orbits      439 444
Stability, Of oscillations      287
Stability, Of the moon’s orbit      417 418
Stability, When the law of force is the inverse $\kappa$ th      298
Stokes, On the figure of the earth      619 Ex. 5
Stokes, Resistance to comets      386
Stone, Longitude is elliptic motion      476
String      545
String of particles, Initial tensions, &c      279
String of particles. heavy suspended particles      305
String passes over a surface      545
Sufficiency, Insufficiency of a first approximation      302
Sufficiency, Of the equations of motion      243
Superposition, Of motions, Theory      271 275
Surface, About steady motion      553
Surface, Cylinders      544
Surface, developable      549
Surface, Ellipsoid      568
Surface, Motion on any surface      535 &c.
Surface, of revolution      541
Surface, Of revolution, the zones      550 &c Surface Paraboloid
Surface, Small oscillations of a heavy particle about lowest point      301
Surface, sphere      542 555
Swarm, Ellipsoidal swarm, page      406
Swarm, Stability of a spherical swarm      414
Sylvester, Motion in a circle      321
Sylvester, Motion in a circle with two centres of force      194
Tait, Brachistochrone when the velocity varies as the distance from the axis of       612 Ex. 4
Tait, Least action in elliptic orbits      651
Tait, Relation of brachistochrones to free paths      591 650
Tautochrone, Examples of tautochronous curves      211
Tautochrone, Linear equation      119
Thomson and Tait, Laws of motion      51
Thomson and Tait, Orthogonal surfaces of trajectories      638
Three attracting particles, Initial radius of curvature      284 Ex. 6
Three attracting particles, Line arrangement      409
Three attracting particles, Motion from rest in either arrangement      413 284
Three attracting particles, Stability      408
Three attracting particles, Triangle arrangement      407
Three attracting particles, Unstable      412
Time, Ambiguities in sign      350 353
Time, Ellipse of small eccentricity      345
Time, Euler’s and Lambert’s theorems      350 352
Time, In a central orbit, ellipse      342
Time, In a central orbit, hyperbola      348
Time, In a central orbit, parabola      349
TIME, In an arc      199 200
Tisserand, Comet in a resisting medium      384 &c.
Tisserand, Criterion of the identity of a comet      415
Tisserand, Disintegration      414
Tisserand, Proof of a theorem of Laplace      487 Ex. 4
Tissot, The conical pendulum      555 note.
Todhunter, Error in a Newtonian problem      134 Ex. 3
Todhunter, On brachistochrones      604
Townsend, Memoir on brachistochrones      591 note.
Train and engine      150 Ex. 5 305
Transon, On hyper-acceleration      233
Two attracting particles, Mass of a planet      402
Two attracting particles, Orbit and time      399
Two centres of force, A circle is a possible orbit $F=\mu u^{5}$       194
Two centres of force, Ellipse described $F=\mu u^{2}$ , tree dimensions      529
Two centres of force, Ellipse described $F=\mu u^{2}$ , two dimensions      355
Two centres of force, Liouville’s general solution      585 &c.
Two centres of force, Liouville’s general solution, in three dimensions      588
Two centres of force. $F=\mu u^{3}$ , lemniscate      587 Ex. 4
Uniform, Angular velocity      41
Uniform, Definition      53
Uniform, Velocity and acceleration      2 15
Units, force      64
Units, Horse-power      72
Units, mass      63
Units, Space and time      46
Units, work      71
Velocity, Components      11
Velocity, In a central orbit from infinity and to the origin      312
Velocity, moment of      6 9
Villarceau, Force in a conic      450 note.
Villarceau, Law of gravitation      390 note.
Vis viva      see Energy.
Vis Viva, Constrained particle      184
Vis Viva, Coriolis on relative vis viva      257
Vis Viva, Deduced from Lagrange’s equations      512 Ex. 3
Vis Viva, Defined      69
Vis Viva, Principle for a fixed field      246
Vis Viva, Principle for rotating field      255
Vis Viva, Vis Viva of a rigid body      253
Work, Central force      186
Work, defined      70
Work, Effective forces      507
Work, Elastic string      187
Work, Rate of doing work      72
Work, Work function      185
Worms, Experiments on Foucault’s pendulum      627
Wythoff, Memoir on dynamical stability      406 note.
Young, Rule for the attraction of table land      208
Zenger, Mean and true anomalies      347 Ex. 2

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