It will simplify the formulas by cancelling a secular term if we make C = A, and the top is then called a spherical top; OH becomes the axis of instantaneous angular velocity, as well as of resultant angular momentum.
When this secular term is restored in the general case, the axis OI of angular velocity is obtained by producing Q′H to I, making
| HI | = | A − C | , | HI | = | A − C | , |
| Q′H | C | Q′I | A |
(3)
and then the four vector components OC′, C′K, KH, HI give a resultant vector OI, representing the angular velocity ω, such that
OI/Q′I = ω/R.
(4)
| Fig. 12. |
The point I is then fixed on the generating line Q′H of the deformable hyperboloid, and the other generator through I will cut the fixed generator OC of the opposite system in a fixed point O′, such that IO′ is of constant length, and may be joined up by a link, which constrains I to move on a sphere.