Dynamics of an Unstabilized Spacecraft During the Deployment of an Elastic Pantograph Structure

Abstract

An unstabilized spacecraft with a pantograph structure deployed in orbit to carry solar batteries is the subject of study. The objective of the study is to construct a mathematical model of this system taking into account the elastic properties of elements of the pantograph in longitudinal and transverse directions. This model is based on the Lagrangian formalism as applied to a mechanical system with rheonomic constraints. The expressions for the coefficients of the equations of motions are obtained using Mathematica 5 © . A Fortran application software package is used for numerical simulation of dynamic processes. This package can be adapted, if necessary, to study other structures. The behavior of the spacecraft during the deployment of the pantograph is numerically analyzed using different values of spacecraft parameters and the parameters of the deployment process in the gravity field.Introduction. The dynamics of reconfigurable systems is one of the promising and important research areas in mechanics [9,[11][12][13]23]. Modern spacecraft incorporate various components that are deployed in orbit (solar batteries (SB), gravity-gradient booms, antennas, etc.). Such mechanical systems are delivered to orbit compactly packaged and then are deployed there. There is literature on the deployment of elastic elements from a fixed base and from a spinning spacecraft [9,[11][12][13]23], including the deployment of a gravity-gradient boom [15,19]. In these studies, the maximum bending moments, deflections of booms, and optimal deployment time were assessed using various simplifying assumptions. Cherchas [14] studied the dynamics of spin-stabilized satellites during the extension of long flexible booms. He has determined the maximum nutation and precession angles after the deployment of the boom and its maximum bending moments and deflections, derived the equations of motion using Lagrange's equations, and discretized the elastic degrees of freedom by a modal analysis. In [20,21,24], the dynamics of deployable elastic elements is also described in terms a modal analysis with time-dependent natural modes.Banerjee and Kane [7] present a new method for simulating the motion of a beam that is being extruded from, or retracted into a rotating rigid body. In essence, the method consists of modeling the beam as a series of elastically connected rigid links and then working with equations of motion linearized in the modal coordinates for the links outside the rigid body. In [6,8], the analysis was extended to large deflections and used an order-n formulation for a variable number of bodies. The modeling has revealed that the tip deflections are very sensitive to the extrusion/retraction rate, the retraction process is less stable than the extrusion process, and the behavior of the beam is strongly dependent on the angular rate of the body.The deployment of such elements is a substantial perturbation to the motion of the spacecraft around its center of mass. It is impossible to model such perturbations within the framework of the...