for a smaller value of R the top cannot spin steadily at the inclination θ to the upward vertical.
Interpreted geometrically in fig. 4
μ = gMh sin θ/CK = An2/KN, and μ = C′K/A sin θ = KM/A,
(8)
KM·KN = A2 n2,
(9)
so that K lies on a hyperbola with OC, OC′ as asymptotes.
4. Suppose the top or gyroscope, instead of moving freely about the point O, is held in a ring or frame which is compelled Constrained motion of the gyroscope. to rotate about the vertical axis OC with constant angular velocity μ; then if N denotes the couple of reaction of the frame keeping the top from falling, acting in the plane COC’, equation (4) § 3 becomes modified into
gMh sin θ − N = μ·CK = sin θ G′μ − Aμ2 cos θ,
(1)