Spinning gas clouds: Liouville integrable cases

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We consider the class of ellipsoidal gas clouds expanding into a vacuum [1, 2] which has been shown to be a Liouville integrable Hamiltonian system [3]. This system presents several interesting features, such as the Painleve property [4, 5], the existence of Backlund transformations and the separability of variables, all shown to be present in at least several sub-cases.