Influence of wind speed on airship dynamics

A new formulation of the equations of motion of an airship is derived to allow the analysis of the wind influence on the airship dynamics. Initially, the equations of motion are written via the Lagragian approach, considering the three kinetic energy terms associated with 1) the energy of the vehicle motion itself, 2) the energy of the air around the airship due to the relative velocities, and 3) the energy added to the buoyancy air. After that, the equations of motion are translated into Newton's second law formulation, yielding a new term, wind-induced force and torque. When the airship geometry approximated by an ellipsoid of revolution is considered the wind-induced terms are then explicitly derived, and their contribution on the longitudinal and lateral dynamics of the airship motion is analyzed. The results are illustrated using the model of a real airship, considering a given range of wind speed and a constant low airspeed.