Shape distortion of space structures, postulates and controversy (Q1825067)

In a previously published papeer [(*) the author, ibid. 39, No.1, 84-95 (1988; Zbl 0629.73081)] a criterion for the shape control robustness of space structures was proposed. However, the general approach applied e.g. in (*) was strictly geometrical. The postulates leading to the method proposed e.g. in (*) are purely geometrical. It must be emphasized that the postulate for distortion introduced in (*) is controversial. For example, e.g. by \textit{R. T. Haftka} [AIAA J. 22, 1293-1298 (1984; Zbl 0562.73081)] a mixed approach is applied. In the definition of the internal distortion the mass of the space structure is involved but the definition of the length of the total internal displacement is geometrical. In this paper a generalization of the definition of shape distortion and static shape control is proposed. It is proven that for full control the controls do not depend on the generalization. A generalization of the measure of robustness is also proposed. Simple numerical examples are presented.