A Treatise on the Theory of Screws

100 THE THEORY OF SCREWS. [106-109 a small initial twisting motion. The twist, and the twisting motion, may each be resolved into their components on the n harmonic screws : n circular pendulums are to be constructed, each of which is isochronous with one of the harmonic screws. All these pendulums are to be started at the same instant as the rigid body, each with an arc, and an angular velocity equal respectively to the initial amplitude of the twist, and to the twist velocity, which have been assigned to the corresponding harmonic screw. To ascertain where the body would be at any future epoch, it will only be necessary to calculate the arcs of the n pendulums for that epoch, and then give the body twists from its position of equilibrium about the harmonic screws, whose amplitudes are equal to these arcs. 107. Remark on Harmonic Screws. We may to a certain extent see the actual reason why the body, when once oscillating upon a harmonic screw, will never depart therefrom. The body, when displaced from the position of equilibrium by a twist upon a harmonic screw 6, and then released, is acted upon by the wrench upon a certain screw r), which is evoked by the twist. But the actual effect of an impulsive wrench on would be to make the body twist about the harmonic screw (§ 104), and as the continued action of the wrench on is indis- tinguishable from an infinite succession of infinitely small impulses, we can find in the influence of the forces no cause adequate to change the motion of the body from twisting about the harmonic screw 0. j