In recent years, a system with rigid and extremely flexible components (hereinafter called "SREF") are often employed for satellite systems in order to realize various vast structures in orbit, and flexible components are made of strings, membrane and so on. In general, flexible component of such a system has two states, one is the state with tensional force and the other is without tensional force. Therefore, state transition of the system arises depending on its configuration, and then careful treatments are required for the analysis of such a system, because number of the combination of state increases dramatically depending on the number of mass and flexible component. Eventually, such an increase of components results in the computational difficulty in the analysis of such a system. Authors have found analogy between the state transition of the SREF and contact problem described by linear complementary problem which was developed by Pfeiffer et al., thus similar procedure can be employed for the analysis of the motion of SREF. In this paper, considering such an analogy and introducing some assumptions, state transition problems for SREF are formulated as liner complementarity problem and effective analysis method for dynamic behavior for SREF is proposed. In order to show the validity of the proposed method, some numerical analyses are performed and physical interpretations of the obtained results are discussed. Furthermore, comparison of the numerical analysis between experimental results shows the validity and advantage of the proposed method.
Recent years have witnessed attempts to employ a system with rigid and extremely flexible components (SREF), usually consisting of strings, membranes, and so on, to realize huge structures for spacecraft in orbit. In general, such flexible components have two states, i.e., with and without tensional force. Previously, the authors proposed an effective method for analyzing SREF motion, which is based on an analogy between the state transitions of the SREF and contact problem of rigid bodies. The state transitions of the SREF are detected via a linear complementarity problem that is used for contact problem in the analysis method proposed by Pfeiffer et al. (Pfeiffer and Glocker, 1996). The authors had applied this method to an SREF consisting of two masses and two strings, where the motion of the system was limited to one dimension. In this study, the method is extended to an SREF having planar motion. As an analysis object, an SREF consisting of two masses and two strings is introduced. Finally, the results of numerical analyses are compared with those of an experiment under same parameters, and the validation of the proposed method is demonstrated by the comparison.
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