摘要
推导出了一组三轴椭球表面积近似计算的级数展开公式,并对应地给出了三轴椭球退化为扁椭球和旋转椭球时的表面积公式。该组公式通过引入偏心率、第三扁率等扁率,使公式结构上更为简洁,具有对称性,进一步完善了椭球表面积的计算理论。验算分析表明,相比于传统的近似公式,给出的近似计算公式的精度显著提高,具有实用价值。
Formulas for the approximate calculation of the triaxial ellipsoid surface area （including the special cases of the oblate or rotational ellipsoids） were derived by series expansion. These formulas are symmetric and have more concise structures by introducing the eccentricity and the third flatting.In this way,the theory for calculating the surface area of all kinds of ellipsoids is improved. Analysis and numerical verification show that the new formulas provided in this study can significantly improve precision and are potential in various applications.
出处
《海洋测绘》
CSCD
2017年第4期15-18,23,共5页
Hydrographic Surveying and Charting
基金
国家自然科学基金(41504031
41631072
41174011
41429401)
东华理工大学江西省数字国土重点实验室开放研究基金(DLLJ201507)
国家973项目(2013CB733305)
关键词
三轴椭球
旋转椭球
表面积
级数展开
第三扁率
triaxial ellipsoid
rotation ellipsoid
surface area
series expansion
the third flattening
