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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 |
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| Предметный указатель |
No forces, when  184
Normal transformations, defined 482
Oscillation, composition and analysis 80
Oscillation, composition and analysis, nearly equal and very unequal 88 91
Oscillation, principal oscillations 53 116
Oscillation, transference 89
Oscillation, transference, about steady motion 111
Oscillation, transference, oscillation about equilibrium 57
Oscillation, transference, with examples 94
Oscillations, small see "Free oscillations" "Forced
Oscillations, small, disc on a plane 244
Oscillations, small, equations of 15
Oscillations, small, of a rod 254
Oscillations, small, sphere on the summit of a fixed surface 231
Oscillations, small, sphere rolls on a surface of revolution 234
Oscillations, small, unsymmetrical suspended body 214
Ostrogradsky, on the deduction of the equations of motion from Least action 449
Owen, drift of shot 210
Owen, on modern artillery 37
Painleve, change of the variable t in Lagrange's equations 458
Pendulum, deviations due to motion of the earth 38
Pendulum, motion in a resisting medium, second approximation 364
Pianoforte, theory given by Helmholtz 620
Poincare, number of algebraic integrals 211
Poinsot, a dynamical experiment 46 Ex.
Poinsot, construction for a body under no forces 143
Poinsot, generalisation 145
Poinsot, measure of the time 198
Poinsot, Polhode 149
Poinsot, Polhode, herpolhode 151
Poinsot, rolling and sliding cone 172
Poinsot, the motion of instantaneous axis in space 168
Poinsot, various theorems 144 171 179 184
Poisson, Bertrand's extension with a proof by Brioschi 497
Poisson, chain suspended by one end 599
Poisson, general theorem that (u, v) is constant 493
Poisson, impact of rods 626
Poisson, motion of a body on a plane 240 249
Poisson, motion of a loose chain 574
Poisson, motion of a top 201
Poisson, motion relative to the earth 34
Poisson, oscillation of a membrane 632
Poisson, oscillation of straight rods 630
Poisson, term of long period in the rotation of the moon 568
Poisson, the determinant in certain dynamical problems cannot have imaginary roots 430
Poisson, variation of parameters 505
Polhode 149
Polhode, Darboux's theorem 150 Ex.
Polhode, Koenigs' theorem 150 Ex.
Polhode, motion when the polhode is small 150 Ex.
Polhode, Sylvester's and Ferrers' dynamical relation 149
Polhode, the separating polhode 149
Polhode, time of describing an arc 150
Potential of the sun and moon at the earth 513
Precession of a top 202 205 210
Precession of the earth 524
Projectiles, deviation due to rotation of the earth 37
Projectiles, falling bodies 35 35
Projectiles, flat and high trajectories 36
Projectiles, theory 33
Puiseux, any solid rotating with axis vertical 252 Ex.
Puiseux, motion of a body on a plane 240
Puiseux, oscillations of an ellipsoid, axis vertical 252 Ex.
Quadric, conditions for a one-signed quadric 60 469
Quality, the difference between the note of various musical instruments 616
Quet, motion of gyroscope 43 46 Ex. 3
Quet, pendulum 39 Ex.
Rayleigh, Lord, effects of an increase of inertia 76
Rayleigh, Lord, motion of a tight string 619
Rayleigh, Lord, on Fourier's rule quoted 400
Rayleigh, Lord, periods of a membrane with a small load 639
Rayleigh, Lord, theorem on the sum of the squared normal functions 630
Reflected waves, at a clamp on a rod 630 Ex.
Reflected waves, at a fixed or loose end 614
Reflected waves, at a junction 622 Ex.
Relative motion, Clairaut's theorem 25
Relative motion, pendulum 38
Relative motion, projectiles 35 37
Relative motion, relative to the earth 33
Relative motion, rigid body 42
Relative motion, rigid body, adaptation of Lagrange's equations 44
Relative motion, rigid body, gyrostat 43
Representative point 128
Representative point, oscillation about equilibrium, path is a straight line 129 130
Representative point, oscillation about steady motion path is an ellipse 134
Representative point, the representative point in a top is the centre of oscillation 201
Representative point, used to represent an oscillation 80
Resals and memoir on Billiards quoted 239
Resistance of the air, boomerang 210
Resistance of the air, no other forces 147
Resistance of the air, pendulum, second approximation 364
Resistance of the air, tight string, thin air, thick air 623
Resistance of the air, top 202
Resistance of the air, uniaxal body 183
Richardson, W.F., tables of deviations of projectiles referred to 37
Rod, chain of rods 419
Rod, how the earth's motion affects the equilibrium of a rod 46 Ex.
Rod, impact of rods 626
Rod, impossible motions 255
Rod, infinite rod 630 Ex.
| Rod, motion of two magnetic rods 94 Ex. 5
Rod, oscillations 254
Rod, periods of vibration of a stretched rod 630 Ex.
Rod, periods of vibration when an inelastic particle falls on a rod 630 Ex.
Rod, transverse vibrations of rods 628
Rod, two rods attached at right angles 630 Ex.
Rod, vibrations of circular rods 631
Roehrs, oscillations of a suspension chain 607
Rolling and sliding cone, definition, equation of 172
Saint-Venant, the impact of rods 626
Salmon, his Solid Geometry quoted 199
Siemens, on Governors referred to 107
Slesser, G.M., motion on a rough plane 240
Slesser, G.M., moving axes 5
Solid body on a plane, any body 245 253
Solid body on a plane, any body, examples 249
Solid body on a plane, oscillations 250
Solid body on a plane, oscillations, stability examples 252
Solid body on a plane, uniaxal body 102 Ex. 241
Sphere, on a revolving plane inclined, horizontal, or vertical 207 208
Sphere, rotating sphere suspended by a string 15 Ex. 117
Sphere, sphere rolls on the inside of a circular ring 234
Sphero-conic, curves described by the invariable line, instantaneous axis and eccentric line 161
Sphero-conic, list of geometrical properties 199
Sphero-conic, velocities along the conic 164
Stability, a body under no forces 155
Stability, conditions for a biquadratic 287
Stability, conditions for a biquadratic, for an equation of the nth degree 290
Stability, Energy test 95 96
Stability, examples 307
Stability, steady motion 113
Stability, two rules to write these 297 301
Stability, vanishing of a subsidiary function 304
Steady motion, analysis of roots 119
Steady motion, analysis of roots, various theorems 120
Steady motion, conditions of stability 113
Steady motion, impulsive forces 118
Steady motion, the determinantal equation 111
Stokes, Sir G., fluorescence 411
Stokes, Sir G., Fraunhofer's dark lines 340
Stokes, Sir G., solution of a differential equation 587
Stokes, Sir G., the roots of the equation  600
Stone, E.J., calculation of two astronomical constants to the third order 531
Stone, E.J., ultimate axis of rotation of a resisted uniaxal body 183 Ex.
String, loose, initial tension of a severed string 592 592
String, loose, oscillation periods of a circular string under a central force 611
String, loose, other examples 593
String, tight, problems on, one string 617
String, tight, several strings in a straight line with or without attached bodies 622 Ex. 11—14
String, tight, strings meeting at a point 622 Ex. 10 15
Sturm, C., theorem on nodes and loops 433
Sylvester, correlated bodies 192
Sylvester, measure of the time 196
Sylvester, top to illustrate the Polhode 149
Symbol (u, v), analytical properties 498
Symbol (u, v), dynamical property 49
Symbol (u, v), Poisson's and Lagrange's forms 490
Thomson, J.J., applications of dynamics to physics and chemistry 461
Tide wave, analogy of the tide wave to a rod 624
Tide wave, relative motion 46 Ex. 7
Tisserand, changing body 22
Todhunter, exceptional cases in maxima 455
Todhunter, string with an impulsive tension 574
Top, cubic surface 204
Top, Hess 212
Top, integrable cases 207
Top, Kowalevski 213
Top, precession 205
Top, stability of a top 103 Ex. 205
Top, tops which can become vertical 202
Top, Tshapliguine 213
Top, why some tops rise on an imperfectly rough ground 243
Transference of energy, Bernoulli's balance 94
Transformation of coordinates, when the equations p'=-dH/dq, q'=dH/dp retain their form, Donkin's and Mathieu's rules 500
Transformation of coordinates, when the equations p'=-dH/dq, q'=dH/dp retain their form, Jacobi's rule 499
Tshapliguine, integral for the motion of some tops 213
Turner, H.H., historical note on the motion of the pole of the earth 534
Uniaxal bodies, a solid of revolution rolls on a solid of revolution 244 Ex.
Uniaxal bodies, conjugate line 183 Ex.
Uniaxal bodies, equations of motion 12
Uniaxal bodies, no forces 180
Uniaxal bodies, Stone's theorem 183 Ex.
Uniaxal bodies, uniaxal tops 200
Uniaxal bodies, various theorems 181
Variation of parameters, comparison 509
Variation of parameters, Lagrange's method 509
Variation of parameters, Poisson's method 505
Vis viva, principle with moving axes 30
Viscosity, principle 333 Ex. 2
Viscosity, tight strings 625
Walker, G.T., bodies which spin in one direction only 253
Walker, G.T., his memoir on the Boomerang quoted 210
Watson, H.W., relative motion 25
Watt's governor, dynamical theory 104
Watt's governor, really a moderator 106
Watt's governor, stability 105
White, W.H., cause of the rolling of ships 341
Williamson, B., the conditions that a quadric is one-signed 60
Willson and Peirce, the roots of the equation 600
Woodward, R.S., Euler's ten-monthly period 540
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