Linearization in satellite attitude control with modified Rodriguez parameters

摘要

If one has the following nonlinear system: Equation 8 [Figure omitted. See Article Image.] Taylor series linearization yields: Equation 9 [Figure omitted. See Article Image.] The higher order terms are neglected. So, the above operation takes the form: Equation 10 [Figure omitted. See Article Image.] In order to correctly linearize the nonlinear system of equation (1), one should derive the Jacobian matrices corresponding to the cross product terms. Those are: Equation 11 [Figure omitted.