In the general motion again of the liquid filling a case, when a = b, Ω3 may be replaced by zero, and the equations, hydrodynamical and dynamical, reduce to
| dξ | = − | 2c2 | Ω2 ζ, | dη | = | 2a2 | Ω1 ζ, | dζ | = | 2c2 | (Ω2 ξ − Ω2 η) |
| dt | a2 + c2 | dt | a2 + c2 | dt | a2 + c2 |
(18)
| dΩ1 | = Ω2 ζ + | a2 + c2 | ηζ, | dΩ2 | = −Ω1 ζ − | a2 + c2 | ξζ; |
| dt | a2 − c2 | dt | a2 − c2 |
(19)
of which three integrals are
| ξ2 + η2 = L − | a2 | ζ2, |
| c2 |
(20)
| Ω12 + Ω22 = M + | (a2 + c2)2 | ζ2, |
| 2c2 (a2 − c2) |
(21)