| ( | A | + c2 ) n2 = μ | CR + K | − μ2 ( | A | + c2 ) + μRρc − g (c − ρ), |
| M | M | M |
(13)
| ( | A | + c2 ) | 2 | n2 = ¼ ( | CK + R | + Rcρ ) | 2 | − g ( | A | + c2 ) (c − ρ). |
| M | M | M |
(14)
Thus for a top spinning upright on a rounded point, with K = 0, the stability requires that
R > 2k′√ {g (c − ρ)} / (k2 + cρ),
(15)
where k, k′ are the radii of gyration about the axis Gz, and a perpendicular axis at a distance c from G; this reduces to the preceding case of § 3 (7) when ρ = 0.
Generally, with α = 0, but a ± 0, the condition (A) and (B) becomes
| ( | C | + a2 ) | Q | = 2μac − Raρ, |
| M | L |