Characterization of non trim trajectories of an autonomous underactuated airship in a low velocity flight

The objective of this paper is to generate a desired flight path to be followed by an autonomous airship. The space is supposed without obstacles. As there is six degrees of freedom and only three inputs for the LSC airship in a low velocity flight, three equality constraints appear due to the under-actuation. When the roll φ and pitch θangles θangles θangles θangles θangles θangles θangles as well as the longitudinal velocity u are imposed, the first constraint gives a differential equation on the yaw angle ψ, ψ, the second equality gives a differential equation on the lateral velocity v and the third one an equation on the vertical velocity w.