测地线密切理论在缓圆曲线的研究

The study on the osculation theory based geodesic line for the spiral-circle curve in highway

本文一开始指出以往高等级交通路线缓圆曲线定位存在的问题,阐述测地线的密切概念和密切特征及其基本条件,说明测地线密切特征对高等级交通路线缓圆曲线密切特征的启示,分析在高等级交通路线运行的车辆逐渐转向运行的密切特征和缓圆曲线组合定位的密切特征。在此基础上,介绍以密切特征理论研究产生的高等级交通路线缓圆曲线定位的二个弧长方程及其解法,指出密切和相切的特征区别,说明密切点是缓圆曲线正确组合定位的依据;指出切点和曲线相切不符合密切特征,以切点的曲线组合不利于高等级交通路线曲线安全定位设计和车辆曲线安全运行。最后,总结测地线密切理论应用研究的四点结论。

In the first part of this paper,the positioning questions in the spiral-circle curve of highway have been introduced,and the osculation concept,the osculation features and its basic conditions of the geodesic line illustrated.This paper presented the inspirations from the osculation features of the geodesic line for the spiral-circle curve in highway.Both the osculation features that the rolling stock turn through the spiral curve gradually and the osculation features that spiral-circle curve made up of the spiral-circle in highway line have been analyzed.And the spiral curve arc-length equation and the middle spiral curve arc-length equation have been developed based on the research of the osculation features in geodesic line.The distinctions have been introduced among the characteristic of the tangent state and the osculation state.According to the characteristic distinctions,this paper proved that the osculation point was the foundation for the exactness combination of the spiral-circle curve.And both the tangent point and the tangent curve were not conformed to the osculation features.The incorrect combination based on the tangent point must be refused from the safe positioning design and safe driving in highway.There are four conclusions have been drawn from the study based on the osculation theory of the geodesic line in this paper.