(a) Applying the principle of conservation of energy, derive a third differential equation...

(a) Applying the principle of conservation of energy, derive a third differential equation for the general motion of the top of Prob. 18.139.

(b)           Eliminate the derivatives from the equation obtained and from the two equations of Prob. 18.139, show that the rate of nutation θ  is defined by the differential equation θ2 = f(θ), where

(c)       Further show, by introducing the auxiliary variable x = cos θ. that the maximum and minimum values of θ can be obtained by solving for x the cubic equation

Fig. P18.140