Subject Index
555
of the airplane, 261–264
departure of a powercraft, 275, 276
particular cases, 193, 229
plane-parallel motion, 193, 239, 253–258
of the airplane, 264, 265
double circular cone, 257
of a rigid straight bar, 255–257
of a sphere, 260
a point of which has an imposed motion,
232–234
rolling on an inclined plane, 269
rolling on a horizontal plane, 271–275
stopping of a powercraft, 275–278
two points of which have an imposed motion,
234–238
Motion of a rigid solid of variable mass, 436
Goddard’s approximate method, 436
motion about the mass centre, 454–457
motion of the aircraft fitted out with jet
propulsion motion, 444
motion in a homogeneous atmosphere, 440
motion of the mass centre, 444, 453
motion of the rocket, 443, 444
motion by simultaneous capture and emission,
442, 443
Oberth’s approximate method, 437–439
theorem of moment of momentum, 449
theorem of momentum, 449
variational methods, 436, 439–441
Motions of the Earth, 381–396
Chandler’s period, 384
diurnal rotation, 382–385
Euler’s cycle, 381–389
free nutation, 390–396
Larmor’s precession, 385
magnetic-mechanical analogy, 385
pseudoregular precession, 390–394
regular precession, 381–389
of revolution, 381, 382
of rotation, 381–383
secular variation, 385–389
Motion of a straight bar, 119
equations of motion, 119–121
longitudinal vibrations, 121, 122
torsional rotations, 121–123
transverse vibrations, 123–128
Motion of threads, 101–119
condition of continuity, 103, 105, 107, 108
equations of motion, 106
forced vibrations, 117, 118
fundamental solution, 115, 116
longitudinal vibrations, 111
transverse vibrations, 111–119
Physical pendulum, 242–247
Bessel pendulum, 248
Borda pendulum, 248–250
determination of moments of inertia, 247
Huygens’s theorem, 242–247
Kater pendulum, 248–250
loxodromic pendulum, 370–372
Mach pendulum, 251, 252
Voinaroski pendulum, 250, 251
Weber-Gauss pendulum, 252, 253
Power, 3, 70
of constraint forces, 4
of external forces, 4
of internal forces, 4
Principles, differential, 41–44
conservation of mass, 86, 87
of d’Alembert, 41
of energy variation, 92
generalized, of Clapeyron, 93
of heat flux, 91
of initial conditions, 90–93
of internal forces, 87–89
of motion of the centre of mass, 96, 97
of objectivity, 85
of variation of the dynamic torsor, 89, 90
of variation of the kinetic torsor, 88
of variation of the moment of momentum, 89, 90
of variation of the momentum, 88, 89
of virtual velocities, 44, 154
of virtual work, 44, 45, 148–155
Problems of motion, 4, 5
of an artificial celestial body, 186–188
of Cayley, 189, 190
of n particles, 32–37, 56–58, 74–77, 182–186
of the rocket, 179–182
of two particles, 35, 36, 56, 57, 182, 183
of the winch, 190–192
Representation of the rotation of a rigid solid, 194
Cayley-Klein parameters, 202–205
Eulerian parameters, 197–201
Euler’s angles, 194, 206, 207
Olinde Rodrigues’s formulae, 199–201
Pauli spin matrices, 203–205
quaternions, 200
spinor, 205
stereographic projection, 200
Strain, 93
System, dynamical, 6
autonomous, 6
non-autonomous, 6
Systems of rigid solids, 459–532
contact of two rigid solids, 471–475
double pendulum, 461–466
motion of a rigid solid on a fixed plane, 477–479
of a heavy circular disc, 493–497
of a heavy gyroscope, 482–485
of a heavy homogeneous rigid solid, 479–482
of a heavy rigid solid of cylindrical form,
485–487
of a heavy sphere, 487–490