Abstract
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.
Highlights
We study the nonlinear dynamics of clusters of tethered satellites via numerical step-by-step time integration of the differential equations of motion
The elastic restoring forces are directly computed at each time step
We write down the dynamic equilibrium equation of the masses of our tethered satellites system via Newton’s Second Law, supposing that we have n generalized coordinates, the three orthogonal free displacements of each mass
Summary
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 the Central Finite Difference explicit method, (Brasil [2][3]). The considered nonlinearities are due to large displacements leading to changes in masses coordinates. The proposed algorithm does not involve assemblage of stiffness matrices. The elastic restoring forces are directly computed at each time step. A cluster of four satellites in a tetrahedral disposition is considered. For tethered satellites, are reported by Cosmo and Lorenzini, [5], Ellis and Hall [7], Kumar [10], Mankala and Agrawal [11], Stevens and Wiesel [18]. Suggestions have been made to future use of carbon nanotubes, as commented by Baughman et al [1]
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