Dynamics of structures of clusters of tethered satellite

In this paper, we study the nonlinear dynamics of clusters of tethered satellites via numerical step-by-step time integration of the differential equations of motion. The basic algorithm is Central Difference explicit method. The masses of the space vehicles are considered lumped and the connection cables are considered massless and of linear elastic material. The considered nonlinearities are due to large displacements leading to changes in masses coordinates. The proposed algorithm does not involve assemblage of stiffness matrices. Instead, the elastic restoring forces are directly computed at each time step. A new time step optimization procedure is implemented. As an example, a cluster of four satellites in a tetrahedral disposition is considered. Free damped vibrations due to large initial conditions are computed.