PURE AND APPLIED MATHEMATICS.
ON THE RELATION BETWEEN THE ANGULAR VELOCITY ABOUT AND THE ANGULAR VELOCITY OF THE INSTANTANEOUS AXIS OF A BODY REVOLVING SPONTANEOUSLY ABOUT A FIXED POINT, AND ON THE AXES OF GREATEST AND LEAST MOBILITY.
By WILLIAM WALTON, M.A., Fellow of Trinity Hall. ET λ, u, v, be the direction-cosines of the instantaneous axis at the end of any time t in reference to a system of fixed rectangular axes of x, y, z, passing through the fixed point. Let be the angular velocity of the body about the instantaneous axis, and let w, w, w, be the components of the angular velocity about the axes of coordinates.
and consequently, differentiating with respect to t, we have
Let r be a given length measured along the instantaneous axis from the fixed point. Then
x=r cosλ, y = r cosμ, z=r cosv,