(18)
where M denotes a constant; so that ψ is an elliptic integral of the second kind.
The quiescent ellipsoidal surface, over which the motion is entirely tangential, is the one for which
| 2 (a2 + λ) | dψ | + ψ = 0, |
| dλ |
(19)
and this is the infinite boundary ellipsoid if we make the upper limit λ1 = ∞.
The velocity of the ellipsoid defined by λ = 0 is then
| U = −2a2 | dψ0 | − ψ0 |
| dλ |
| = | M | − ∫∞0 | M dλ |
| abc | (a2 + λ)P |
| = | M | (1 − A0), |
| abc |