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三维井眼轨道设计问题需要求解多元非线性方程组,由于未知数多、方程的非线性强,一般难以求出解析解,通常使用数值迭代方法求数值解.对三维s型轨道设计问题依据已知设计参数进行了分类,发现了一套有效的数学化简技巧,求出了第1类初值问题的解析解和第Ⅱ-Ⅳ类初值问题的拟解析解.提出了轨道设计问题的特征多项式的新概念,并证明了轨道设计问题是否有解取决于特征多项式是否有实数根,解的个数不多于实数根的个数或个数的二倍.所提出的基于特征多项式实数根的拟解析算法对于求解轨道设计问题具有计算速度快、计算可靠性高、易于计算机编程实现等优点,在三维水平井轨道设计、三维绕障井轨道设计、防碰设计等方面具有比数值迭代方法更好的计算性能.
Due to the large number of unknowns and the strong nonlinearity of the equations, it is generally difficult to find the analytical solution, and the numerical iteration method is usually used to solve the numerical solution. The design of the three-dimensional orbital trajectory is based on the known Design parameters are classified and an effective set of mathematical simplification techniques is found, and the analytic solution of the initial value problem of the first kind and the quasi-analytical solution of the initial value problem of the Ⅱ-Ⅳ kind are obtained. The characteristics of the orbit design problem And prove whether the orbital design problem is solved depends on whether the characteristic polynomial has real roots or not, the number of solutions is no more than twice the number or number of real roots. The proposed polynomial-based polynomial roots The quasi-analytic algorithm has the advantages of fast computation speed, high computational reliability and easy programming by computer. It has many advantages over numerical iteration methods in three-dimensional horizontal well trajectory design, 3D bypass well trajectory design and anti-collision design, Better computing performance.