In this paper, a new approach to the modelling of the deployment dynamics of a flexible multi-body system with the time dependent configurations is demonstrated in the frame of the study the dynamics of a spacecraft with the gyro-gravitational system of stabilization. Primarily the gravitational stabilizer that is made as a pantograph structure is in a compact form. The deployment of a flexible pantograph structure is performed after placing the spacecraft into orbit and completion of the preliminary damping by a special jet-propelled system, and after uncaging the gyros. After its deployment, the pantograph turns into an elongated structure that serves as a gravitational stabilizer and carrier of solar batteries. The objective of the study is the creation of the generalized mathematical model and the conducting of the computational modelling of the spacecraft dynamics. The equations of motion are derived with the use of the Eulerian-LaGrangian formalism and symbolic computing. Numerical simulations of the typical operational mode of the system are conducted taking into account various control profiles for the deployment. Numerical results indicate that the system used for attitude stabilization ensures the shape of the deployed design and prescribed accuracy of the orientation. 1. Introduction Structures created from elements delivered into orbit in a compact condition are one of the basic components of modern space systems. Spacecraft (SC) with long flexible appendages for the exploration of the Earth’s physical fields and gravitationally stabilized SC that deploys the long boom with the mass concentrated at the tip have been used since the end of the fifties of the previous century. The deployment of the space structures brings in considerable disturbances into the dynamics of the SC about its mass centre. At present, the study of such deployable structures is actually for minimization of deployment duration and power resources, for analysis of the effect of attached systems of a changeable configuration on the SC attitude. The problem of weight reduction of such systems is constantly actual. Therefore, elements of such systems should be considered as elastic bodies. There is a large number of studies in the literature dedicated to the deployment of elastic appendages from the fixed basis as well as from the rotating SC [1–6], including the deployment of the gravity-gradient boom [7, 8]. The maximum bending moments and the deflection of the booms at different simplifying hypothesis were evaluated in these papers; the optimization of the boom
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