Abstract
Ovsiannikov [Dokl. Akad. Nauk SSSR 111 (1965)] and Dyson [J. Math. Mech. 18 (1968) 91] have proposed a model of an ellipsoidal gas cloud adiabatically expanding into a vacuum, and have shown that the equations of fluid motion are thereby reduced to a set of ordinary differential equations, of order 18 in the most general case. Gaffet [J. Fluid Mech. 325 (1996) 113] has shown that their integration reduces to quadratures (if the gas is monatomic and there is no rotating motion of the ellipsoid’s principal axes), as a result of the existence of two integrals of the motion, m and I2. In the present work we establish the minimum value m0(I2) of m, compatible with the existence of physically meaningful solutions. We succeed in performing the separation of variables, and obtain the unexpected result that, when the energy integral m takes its minimum value m0(I2), the general solution of the equations of motion is described by elliptic functions.
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