L = ½ (1 − κ) + λp/n,
(28)
so that p = 0 and the motion is made algebraical by taking L = ½ (1 − κ).
The stereoscopic diagram of fig. 12 drawn by T. I. Dewar shows these curves for κ = 15⁄17, 3⁄5, and 1⁄3 (cusps).
10. So far the motion of the axis OC’ of the top has alone been considered; for the specification of any point of the body, Euler’s third angle φ must be introduced, representing the angular displacement of the wheel with respect to the stalk. This is given by
| dφ | + cos θ | dψ | = R, |
| dt | dt |
(1)
| d(φ + ψ) | = ( 1 − | C | ) R + | G′ + G | , |
| dt | A | A (1 + cos θ) |
| d(φ − ψ) | = ( 1 − | C | ) R + | G′ − G | . |
| dt | A | A (1 − cos θ) |
(2)