Modeling and numerical simulation of linear and nonlinear spacecraft attitude dynamics and gravity gradient moments: A comparative study

In this paper linear and nonlinear models of spacecraft attitude dynamics equations and gravity gradient moments are investigated. In addition, effects of gravity gradient moments on attitude dynamics of the satellite are studied. The purpose of this paper is to present a comparison between nonlinear and linear models of spacecraft attitude dynamics and gravity gradient moments in order to determine divergence of linear approximation from the nonlinear model. Simulation results indicate that designer of spacecraft attitude control subsystem should be meticulous in applying linear approximation of equations especially in low earth orbits. Consequently, finding an upper bound for small angle to keep the linear model valid and precise enough would be a vital part of using linear approximation. Results supported by numerical examples demonstrate various features of this study.

► Spacecraft attitude dynamics and gravity gradient moments are modeled in two forms of linear and using Euler angles.
► By using numerical simulation a comparative study is presented such that it is useful for practical application.
► We show that designer should be careful about using the linear or nonlinear forms of spacecraft attitude equations especially in low earth orbits.
► In this way one may find an upper bound for value of small angle term which the linear model is valid.
► The designer or control engineer must find a value of small angle by according to desired accuracy.