| 旋转椭球面上的应变与转动张量表达 |
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| 引用本文： | 刘序俨,黄声明,梁全强.旋转椭球面上的应变与转动张量表达[J].地震学报,2007,29(3):240-249. |
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| 作者姓名： | 刘序俨 黄声明 梁全强 |
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| 作者单位： | 1) 中国福州350003福建省地震局2) 中国厦门361021厦门地震勘测研究中心 |
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| 摘 要： | 以旋转椭球体面上某点为原点建立一个大地坐标单位活动坐标架. 通过平移, 使活动坐标架的原点与以椭球中心为原点的笛卡尔单位标架的原点相重合. 然后再通过两次标架旋转, 使活动坐标架与笛卡尔单位标架完全重合. 本文给出了使两个单位标架相重合的转换关系式, 以及该点位移在两个单位标架中的坐标转换式； 在此基础上, 考虑该点的位移及活动坐标架皆为该点大地坐标的函数, 经复杂推导, 分别给出了该点位移向量的微分在大地坐标系中的分量以及该点分别沿坐标曲线的弧微分表达式, 继而导出了该点的位移梯度矩阵; 最后推导出了椭球坐标系的应变张量与转动张量表达式, 并对转动张量的几何含义进行了较详细的解释, 且采用曲面理论对球面与椭球面的应变张量间的内在关系进行了讨论.
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| 关 键 词： | 活动坐标架 椭球大地坐标系 应变张量 转动张量 |
| 文章编号： | 0253-3782(2007)03-0240-10 |
| 修稿时间： | 2006年11月8日 |
EXPRESSION OF STRAIN AND ROTATION TENSOR IN GEODETIC COORDINATES |
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| Liu Xuyan,Huang Shengming,Liang Quanqiang.EXPRESSION OF STRAIN AND ROTATION TENSOR IN GEODETIC COORDINATES[J].Acta Seismologica Sinica,2007,29(3):240-249. |
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| Authors: | Liu Xuyan Huang Shengming Liang Quanqiang |
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| Abstract: | In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordinates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellipsoid are also discussed. |
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| Keywords: | moving trihedron geodetic coordinates strain tensor rotation tensor |
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