Abstract Reflectors are very critical space elements and can be used not only as solar collectors/reflectors, telecommunication radio antennas and telescopes but also for dual-usage such as solar sails and solar concentrators to probe and sublimate materials from asteroids when actively controlling the surface shape. In this paper, the surface shape of a slack reflector with negligible elastic deformations will be controlled to be a paraboloid by actively modulating the solar radiation pressure (SRP) force using reflectivity control devices (RCDs) across the reflector. Nonlinear static equilibrium equations for an arbitrary infinitesimal within the reflector along the radial, circumferential and transverse directions are established considering the external modulated SRP force and internal tensions respectively. The coupled radial stress differential governing equation and reflectivity algebraic equation are obtained for the paraboloid reflector by the help of the formulation of an inverse problem based on equilibrium equations previously established. Some analytical and numerical analysis for reflectors with ideal and non-perfect SRP force models are performed respectively. The conclusions concerning about how to control the reflector’s surface shape successfully using allowed reflectivity, resulting in reasonable stress range, moreover, how to get the feasible solutions influenced by the reflector’s size parameters, are all based on the presented analytical and numerical analysis.

中文翻译：

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由利用调制太阳压力的副反射器组成的集成抛物面空间反射器的表面形状控制

摘要 反射器是非常关键的空间元素，不仅可以用作太阳能收集器/反射器、电信无线电天线和望远镜，还可以作为太阳帆和太阳能聚光器等双重用途，在主动控制表面形状的同时探测和升华来自小行星的物质。 . 在本文中，弹性变形可忽略不计的松弛反射器的表面形状将通过使用反射器上的反射率控制装置 (RCD) 主动调制太阳辐射压力 (SRP) 力来控制为抛物面。分别考虑外部调制的SRP力和内部张力，建立了反射器内沿径向、周向和横向方向的任意无穷小的非线性静态平衡方程。借助基于先前建立的平衡方程的逆问题的公式化，获得了抛物面反射器的耦合径向应力微分控制方程和反射率代数方程。分别对具有理想和非完美 SRP 力模型的反射器进行了一些解析和数值分析。关于如何利用允许的反射率成功控制反射器表面形状，从而得到合理的应力范围，以及如何得到反射器尺寸参数影响的可行解的结论都是基于所提出的解析和数值分析。