Solution of reentry trajectory with maximum cross range by using Gauss pseudospectral method

The Gauss pseudospectral method(GPM) is used to solve the reentry trajectory of the lifting vehicle with the maximum cross range.The trajectory optimal problem of three-dimension reentry for the vehicle is transformed into a nonlinear programming problem through GPM with differential form.During solving the optimal trajectory,the state and control variables on Gauss nodes are chosen as parameters to be optimized,and the optimal performance index is the maximum cross range.By comparison,the reentry trajectory which is solved by GPM is better than that by the maximum L/D ratio method.Moreover,the simulation process indicates GPM is not sensitive to the estimate of motion states and is easier to converge,and thus it is effective to solve trajectory optimization problems.