(a) Applying the principle of conservation of energy, derive a third differential equation for the general motion of the top of Prob. 18.137.

(b) Eliminating the derivatives φ and ψ from the equation obtained and from the two equations of Prob. 18.137, show that the rate of notation θ is defined by the differential equation 2 θ = 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

Transcribed Image Text:

2E- 5 (4) - + (28_42² - 2gr-coase) - (1 - Boese ƒ(0) = 2E 1 I'sine - B² I Z -2mgex 0 (1-x²)-(a-px)² = 0 (1) (2)