The change trend of state variables,such as flight speed,velocity angle,longitudinal range,altitude,for hypersonic glide vehicle under the condition of skip glide are studied.The numerical solutions of the vehicle state variables are obtained with the fourth-order Runge-Kutta method.The numerical solutions of state variables are fitted with different order orthogonal polynomials,and the analytical solutions representing the variation trend of the state variables are solved.The simulation results show that the mean difference of the root mean square error (RMSE) of the three analytic solutions of flight speed,velocity angle and altitude is 20 m/s,0.1° and 1.5 km respectively,so the variation trend of flight speed,velocity angle and altitude under the skip glide condition can be expressed by the first order orthogonal polynomial.The RMSE of the first order analytic solution of the flight longitudinal range is obviously larger than that of the second order analytic solution and the third order analytic solution,so the flight longitudinal range under the skip glide condition can be expressed by the second order or the third order orthogonal polynomial.

The solutions of flight speed,path angle,longitudinal range,altitude for hypersonic glide vehicle under the condition of equilibrium glide are studied.The analytical expressions between flight speed,longitudinal range,altitude and flight path angle are obtained by theoretical derivation,and the numerical solution of flight path angle is obtained by fourth-order Runge-Kutta method.The approximate solution of flight path angle is obtained by using curve fitting theory.The simulation results show that there is a nonlinear relationship between flight path angle and flight time under the condition of equilibrium glide,and the analytical solutions of flight speed,longitudinal range and altitude can well characterize the numerical solution.