Analytical solutions of steady glide trajectory for hypersonic vehicle and planning application

A kind of analytical solving method for the three-dimensional steady glide trajectory of the hypersonic vehicle is presented in this paper for the online planning problem. Firstly, the lift coefficient is separated into three components of lateral component, steady glide normal component and equilibrium glide normal component. Then, the longitudinal trajectory, lateral trajectory and velocity are decoupled in the dynamics. After that, the solutions of height, downrange and velocity azimuth angle are obtained by the analytical integration and the regular perturbation method, while the solutions of longitude, latitude and velocity are obtained by the Gaussian quadrature and single-step Runge-Kutta integration separately, and the accuracy of those solutions are improved by increasing the computational steps. Finally, a rapid steady glide trajectory programming algorithm is proposed based on the above analytical solutions, and the planning parameters are the lateral lift coefficient and steady glide normal lift coefficient. The simulation results show that those analytical solutions are more accurate than the Bell's solutions, and the planning algorithm only needs a small amount of calculation and obtains the result quickly, which can be used for online trajectory planning.