椭球面大地测量学的非欧几何特性研究

项目名称： 椭球面大地测量学的非欧几何特性研究

项目编号： No.41504031

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 天文学、地球科学

项目作者： 过家春

作者单位： 安徽农业大学

项目金额： 18万元

中文摘要： 前期研究表明椭球面大地测量学的理论方法具有明显的非欧几何特性。当前，关于椭球面大地测量学的论述一般都基于欧氏几何原理。在基于欧氏几何原理的椭球面大地测量的理论与实践中，由于没有建立非欧几何的理论体系，许多椭球面大地测量问题都变得更为复杂，甚至难以表述。本项目拟运用非欧几何原理，围绕曲率与弧长、大地线与大地主题解算、坐标转换与地图投影等相关问题开展研究，分析椭球大地测量学的非欧几何特性，并应用3M数学软件（Mathematica、Maple、Matlab）进行相关原理方法的推导、求证、分析与模拟，实现基于非欧几何与欧氏几何的椭球面大地测量的转换关系，为大地测量学相关领域的应用提供理论依据和应用基础。

中文关键词： 椭球面大地测量学；非欧几何；微分几何；黎曼几何

英文摘要： Previous studies have been showed that the theories and methods of ellipsoidal geodesy have significant characteristics of non-Euclidean geometry. At present, about the ellipsoidal geodesy discussions are generally based on Euclidean geometry principle. In the theory and practice of ellipsoidal geodesy based on Euclidean geometry principle, due to lack of non-Euclidean geometrical establishment, many problems of ellipsoidal geodesy has been more complicate and unclear description. Concentrating on curvature and arc length, geodesic, geodetic problems, coordinate transformation, and map projection by non-Euclidean geometry principle, the project would analyze the non-Euclidean geometrical characteristics of ellipsoidal geodesy, and would obtain the derivations, verifications, analysis and simulations of related principles. The project would realize the ellipsoidal geodesy conversion relationships based on non Euclidean geometry and Euclidean geometry and would provide theoretical and application basis for geodesy.

英文关键词： Ellipsoidal Geodesy;Non-Euclidean Geometry;Differential Geometry;Riemannian Geometry