Low-Order Model of Spin Type Solar Sail Dynamics by Empirical Model Reduction

Abstract

The paper will try to discuss the issue of reducing the time to calculate the nonlinear dynamics simulation of the gossamer structure, especially for the solar sail, because one of the problems in the gossamer structure is design time reduction. Therefore the present paper describes the low-order model of a spin type solar sail dynamics. The model reduction technique is required to shorten the design period. However there is no model reduction methodology about the solar sail dynamics. In this paper the full-order model of a spin type solar sail craft is modeled by geometrically nonlinear FEM based on the energy momentum method (EMM), so the numerical time integration is unconditionally stable. The low-order model is constructed by an empirical model reduction method. To conserve the geometrical relation of constraint conditions on the low-order space, we constructed a penalty method for the geometrical constraint based on the EMM. We will show the reduction model of the spin type solar sail model can approximate the full-order model with sufficient accuracy. Nomenclature d C = covariance matrix m i e = nodal base vector () E = expectation x m  f = modified vector of the internal force corresponding to the nodal position vector m x m   f = modified vector of the internal force corresponding to the finite rotation vector m  x m  F = modified vector of external force corresponding to the nodal position vector m x m   F = modified vector of external force corresponding to the finite rotation vector m  H = total energy i i = orthonormal vector = () 123 ,, T