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Equilibrium configuration of a bounded inextensible membrane subject to solar radiation pressure


The equilibrium shape of a thin inextensible membrane subject to solar radiation pressure under given boundary constraints is studied. The membrane is assumed to be insusceptible to elastic deformation and to have negligible bending resistance, and its steady-state shape is therefore described by a developable surface (i.e., a surface of zero Gaussian curvature), resulting from an equilibrium between radiation pressure and membrane tension forces. A quantitative understanding of the mechanics of such membranes is essential in characterizing the dynamics of solar sail spacecraft that use sail wing tip displacement as an attitude control mode. The analysis in this paper develops a theoretical foundation for the billowed wing shape. Under reasonable simplifying assumptions, the key result is that solar radiation pressure and a given wing tip displacement yield a billowed solar sail wing with the shape of a generalized cylinder (i.e., a developable ruled surface, whose rulings are all parallel, rather than a general developable with variable ruling directions). The base curve geometry for the solar sail is also determined as the solution to a boundary value problem. The results presented herein allow the shape of the billowed membrane to be computed to any desired precision, for any given tip displacement.

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