A new concept of airship without thrust, elevator or rudder is considered in this paper. It is actuated by a moving mass and an internal air bladder with adjustable mass. This results into the motion of the center of gravity and the change of the net lift. The development of this concept of airship is motivated by energy saving. The moving mass and the airshipʼs rigid body are viewed independently, which renders the modelling easy and displays clearly the interconnection of the two subsystems. An eight degrees-of-freedom (DOF) complete nonlinear mathematical model of this airship is derived through the Newton-Euler approach. The dynamics in the vertical plane are analyzed and controlled, using maximal feedback linearization. The modelling, analysis, and control are solved for special cases of the airship which become gradually complex. The most constrained case reduces to a two-DOF system. It is shown that the basic properties of this two-DOF mechanical system remain instrumental for the analysis and synthesis of advanced airships. These properties are far from being obvious when the most complex model is considered.