| Expression of strain and rotation tensor in geodetic coordinates |
| |
| 作者姓名： | 刘序俨 黄声明 梁全强 |
| |
| 作者单位： | Earthquake Administration of Fujian Province，Earthquake Administration of Fujian Province，Xiamen Research Center of Earthquake Surveying Fuzhou 350003 China，Fuzhou 350003 China，Xiamen 361021 China |
| |
| 摘 要： | 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 coordi-nates. 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 ellip-soid are also discussed.
|
| 关 键 词： | 大地座标 应变张量 转动张量 移动三面体 表达式 |
| 文章编号： | 1000-9116（2007）03-0254-11 |
| 收稿时间： | 2006-11-08 |
| 修稿时间： | 2007-02-26 |
Expression of strain and rotation tensor in geodetic coordinates |
| |
| Liu Xü-yan , Huang Sheng-ming and Liang Quan-qiang.Expression of strain and rotation tensor in geodetic coordinates[J].Acta Seismologica Sinica(English Edition),2007,20(3):254-264. |
| |
| Authors: | Liu Xü-yan Huang Sheng-ming and Liang Quan-qiang |
| |
| Institution: | (1) Earthquake Administration of Fujian Province, Fuzhou, 350003, China;(2) Xiamen Research Center of Earthquake Surveying, Xiamen, 361021, China |
| |
| 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 coordi- nates. 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 ellip- soid are also discussed. |
| |
| Keywords: | moving trihedron geodetic coordinates strain tensor rotation tensor |
| 本文献已被 CNKI 维普 SpringerLink 等数据库收录！ |
