Comment on “Three-Dimensional Ascent Trajectory Optimization for Stratospheric Airship Platforms in the Jet Stream

摘要

LEE and Bang [1] have recently analyzed optimal trajectories ofnan airship in the jet stream using a nonlinear point mass modelndeveloped in the relative wind frame. Using a point mass model fornthe elongated airship implies that the airship’s yawwith respect to thenrelative wind frame is always zero; i.e., the side slip angle is zero.nThis is also demonstrated by the absence of side slip in the aerody-nnamic model. For the analysis in [1] a point mass model is adequatenfor analysis because the relative heading , flight path angle u0001, andnbank angle u0002 are slowly varying such that the rotational dynamics cannsafely be ignored. Unfortunately, in forming the point mass model,nthe authors improperly consider the contribution from the addednmass of the airship. In general, the added mass should be treated as antensor in formation of the dynamics [2,3]. In [1] the tensor propertiesnof added mass are ignored and diagonal elements of the added massnmatrix are added together along with the actual mass to form a scalarntotalmassmT. In addition, the addedmass contribution is considerednproportional to the inertial velocity of the airship rather than thenrelative airspeed.