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Published online by Cambridge University Press: 15 September 2014
The object of this note is to obtain briefly the intrinsic equations of motion of a gyroscope, and to show how they lead immediately to the solution of a number of problems. So much has been written on the subject of the gyroscope that these equations are hardly likely to be new, but I do not remember to have met with them in their explicit form. Apart from their use as a basis for calculation, they have a simple interpretation which enables us to foresee the general character of the motion in cases where the actual calculation would be difficult.
page 154 note * The figure is simplified by the assumption that C' may be taken to lie in CA. The error thus involved, and in the consequent positions of A', B', is of the second order, and so does not affect the final results.
page 154 note † There is also an obvious interpretation of (5) in terms of the two-dimensional dynamics of a particle; but this is, as a rule, less convenient for our purpose.
page 155 note * This case occurs in Hydrodynamics, in the motion of a cylinder with cyclic irrotational motion about it, and subject to a constant force such as gravity. Again, in Electricity we have the case of an electron moving in a field where the electric and magnetic forces are uniform and at right angles to one another.
page 158 note * So that 2π/p is the period of oscillation when n = 0.
page 159 note * The matter is treated very fully by Noether, F. in Klein and Sommerfeld's Theorie des Kreisels, pp. 794et seq.Google Scholar
page 160 note * Round numbers have been taken, but the order of magnitude is in each respect the same as in a practical example given by Klein and Sommerfeld, p. 832.
page 161 note * Where the rotation of the flywheel is supposed to be counter-clockwise as viewed from above.
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