| 三轴椭球表面积的近似计算 |
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| 引用本文： | 过家春,申文斌,边少锋,纪兵.三轴椭球表面积的近似计算[J].海洋测绘,2017(4):15-18. |
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| 作者姓名： | 过家春 申文斌 边少锋 纪兵 |
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| 作者单位： | ;1.武汉大学测绘学院;2.安徽农业大学理学院;3.海军工程大学导航工程系 |
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| 基金项目： | 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) |
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| 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。
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| 关 键 词： | 三轴椭球 旋转椭球 表面积 级数展开 第三扁率 |
Approximate Calculations for the Surface Area of Triaxial Ellipsoid |
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| GUO Jiachun,SHEN Wenbin,BIAN Shaofeng,JI Bing.Approximate Calculations for the Surface Area of Triaxial Ellipsoid[J].Hydrographic Surveying and Charting,2017(4):15-18. |
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| Authors: | GUO Jiachun SHEN Wenbin BIAN Shaofeng JI Bing |
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| Abstract: | 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. |
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