sin θ exp (ψ + pt)i = i√ [(−z1 − z3) (z − z2)] + √ [(z3 − z) (z − z1)],
| z2 = | 1 + z1 z3 | , √ | −z1 − z3 | = | G | = | p | = | G′ | . |
| z1 + z3 | 2 | 2An | n | 2Anz1 |
(22)
Thus z2 = 0 in (22) makes G′ = 0; so that if the stalk is held out horizontally and projected with angular velocity 2p about the vertical axis OC without giving any spin to the wheel, the resulting motion of the stalk is like that of a spherical pendulum, and given by
| sin θ exp (ψ + pt)i = i √ ( | 2p2 | cos θ ) + √ ( sin2 θ − 2 | p2 | cos θ ), |
| n2 | n2 |
= i sin α √ (sec α cos θ) + √ [(sec α + cos θ) (cos α − cos θ)],
(23)
if the axis falls in the lowest position to an angle α with the downward vertical.
With z3 = 0 in (21) and z2 = −cos β, and changing to the upward vertical measurement, the motion is given by
sin θ eψi = eint √ ½ cos β [√ (1 − cos β cos θ) + i√ (cos β cos θ − cos2 θ)],