Chapman方程同伦分析方法求解研究

Chapman方程是再入领域的经典方程,适用于对航天器再入轨迹规律的研究,但难以得到其解析解,故提出利用同伦分析方法(HAM)求解Chapman方程解析解。将平衡滑翔再入近似解析解作为HAM的初始猜测解形式,并通过选取合适的辅助线性算子和基函数,得到Chapman方程在小升阻比下的同伦解。仿真结果表明,基于HAM得到的解析解与数值解能够很好地吻合,验证了该方法的有效性和精确性。

Research on homotopy analysis method for Chapman equation

Chapman equation, a classical equation in reentry field, suits for the qualitative analysis of the reentry trajectory, but it is difficult to get its analytical solution.In this paper, homotopy analysis method (HAM) was proposed to solve it.The HAM solution of the Chapman equation in the case of low lift-to-drag radio was obtained by utilizing an approximate solution of equilibrium gliding entry as the form of the initial guess solution, and selecting the proper auxiliary linear operator and the proper basic function.The simulation results show that the analytical solution based on HAM coincide well with the numerical solution, which verifies the effectiveness and accuracy of this method.