公路缓和曲线弧长的精确解及其应用

根据微分几何理论,按反分析原理,从缓和曲线的整体结构关系中推证了缓和曲线弧长基础方程的形式。该文同时利用现代数学与测量平差理论的研究成果,分析缓和曲线弧长基础方程的收敛性质,提出直接精确求解缓和曲线弧长的迭代方法.介绍应用缓和曲线弧长方程求解弧长的技术方案“弃A取p”,突破“参数估计法”的技术难点,为缓和曲线的应用提供“精确、简便”的新技术思路.缓和曲线弧长基础方程的提出及其解法和应用试验表明,缓和曲线没有理想精确弧长方程的历史已经结束;缓和曲线弧长基础方程在缓和曲线弧长直接精确求解和各种曲线组合定位中具有独特优点和显著的通用特征.

The Research for the Arc-length Equation of the Spiral Curvein Highway

According to the differential geometry theory and counter-analysis principle,this paper deduces the spiral curve arc-length base equation of higher degree from its total construction.Applying the theory about the modern mathematics and the survey adjustment,it analyses the astringent properties in the arc-length base equation of the spiral curve and advances a method-the iterative method to get the arc-length of the spiral curve directly and precisely.Applying the technologyical project on "p substitute for A",making a breakthrough at the old and trouble method-"parameter estimate method "0,getting the arc-length of the spiral curve,the new technological project is used in the highway.There are some conclusions in this paper: the history that no arc-length base equation for the spiral curves has been closed;it is important that the special characteristics of the arc-length base equation may be employed universally in the curve composing and positioning.