同伦方法及飞机非线性平衡状态确定

运用同伦方法的基本思想研究飞机非线性平衡状态的求解。首先给出不同伦微分方程组的构造方法及解曲线跟踪算法的实现方法，然后针对目前典型同伦算法的不足，给出一种新的同伦算法。并对飞机运动的六自由度非线性方程组平衡解的实例计算，证实这一算法的可行性和有效性，以及在速度和精度上较之某些传统方法的巨大优越性，成功地克服了工程实际中非线性方程传统解法通常存在局部收敛的局限性。

Homotopy Method for the Calculation of Nonlinear Equilibrium Equations of Aircraft

In this paper, the method of solving nonlinear equilibrium state of aircraft is studied according to homotopy concept. The construction method of homotopic differential equations and a new solution following curve algorithm are also given which succeed in calculation of the nonlinear equilibrium equations of aircraft. The results show that the new algorithm is superior to some traditional methods in calculating velocity and accuracy, and has no special requests to the initial points.