论文部分内容阅读
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。首先给出了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估算法的不足，给出一种新的同伦算法。并通过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。
Study on the Solution of Nonlinear Equilibrium State of Aircraft Using the Basic Idea of Homotopy Method. Firstly, the construction method of the homotopy differential equations and the method of solving the curve tracing algorithm are given. Then a new homotopy algorithm is given for the deficiency of the current typical estimation method. Through the calculation of the example of the equilibrium solution to the nonlinear equations with six degrees of freedom, the feasibility and validity of this algorithm and the great superiority in speed and accuracy over some traditional methods are proved. It successfully overcomes the limitations of the traditional convergence method of nonlinear equations in engineering practice.