and drawing GL vertically upward of length λ = g/μ2, the height of the equivalent conical pendulum, the steady motion condition may be written
(CR + K) μ sin α − μ2 sin α cos α = −gM (a cos α − c sin α)
+ M (μ2c sin α − μRa) (a sin α + c cos α)
| = gM [bλ−1 (a sin α + c cos α) − a cos α + c sin α] = gM·PT, |
(11)
LG produced cuts the plane in T.
Interpreted dynamically, the left-hand side of this equation represents the velocity of the vector of angular momentum about G, so that the right-hand side represents the moment of the applied force about G, in this case the reaction of the plane, which is parallel to GA, and equal to gM·GA/GL; and so the angle AGL must be less than the angle of friction, or slipping will take place.
Spinning upright, with α = 0, a = 0, we find F = 0, Q = 0, and
| − | CR + K | + 2μ ( | A | + c2 ) − Rcp = 0, |
| M | M |
(12)