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A new concept stratospheric aerostat is investigated which consists of a saucer-shaped hull, multi-vectored thrusters, and an under-slung nacelle. The design of this aerostat involves tradeoffs between conventional airship and high altitude balloon. The sling connection simplifies structure design significantly, but brings challenges for dynamics analysis. Dynamics modeling for this aerostat is a kind of double-body problem with geometric constraint. Nonlinear dynamics model is established by considering the effects of under-slung nacelle. Oscillation behavior of this double-body system is superposed by a long-period oscillation of the hull and a short-period oscillation of the nacelle. The length of sling only influences the short-period oscillation but the mass ratio of nacelle to main body determines the stability of system. Finally, an envelope about mass ratio and maximal open loop forward thrust as well as speed is presented, where the system is stable.