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 ...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.展开更多
A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coor...A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coordinate parameters,but the two families of coordinate curves were still meridians and parallel circles.The first fundamental form on the ellipsoidal surface and its three coefficients were deduced by the geodesic coordinate.The formula for the latitudinal scale factor of length for geodetic parallel lines was derived,by which the obtained result conformed to that standard value calculated from geodetic latitude,and it is applicable in the range of 400 km from north to south.Therefore,it lays the foundation for establishing the differential equation and differential relationship based on this type of coordinate parameters;and consequently,it is convenient and accurate enough to operate on the ellipsoidal surface in this new form of geodetic coordinate system.展开更多
It is the main task of the antarctic surveying expedition to establish the surveying system. In three times of the antarctic surveying research expeditions, a complete and accurate surveying system has been establishe...It is the main task of the antarctic surveying expedition to establish the surveying system. In three times of the antarctic surveying research expeditions, a complete and accurate surveying system has been established in the Chinese Great Wall Station area. The surveying system includes geodetic coordinate system, elevation system and gravity reference system. In this paper, the surveying methods and the mathematical models for establishing these systems are discussed, and the accuracy of results is analysed.展开更多
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.40471114).
文摘A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coordinate parameters,but the two families of coordinate curves were still meridians and parallel circles.The first fundamental form on the ellipsoidal surface and its three coefficients were deduced by the geodesic coordinate.The formula for the latitudinal scale factor of length for geodetic parallel lines was derived,by which the obtained result conformed to that standard value calculated from geodetic latitude,and it is applicable in the range of 400 km from north to south.Therefore,it lays the foundation for establishing the differential equation and differential relationship based on this type of coordinate parameters;and consequently,it is convenient and accurate enough to operate on the ellipsoidal surface in this new form of geodetic coordinate system.
文摘It is the main task of the antarctic surveying expedition to establish the surveying system. In three times of the antarctic surveying research expeditions, a complete and accurate surveying system has been established in the Chinese Great Wall Station area. The surveying system includes geodetic coordinate system, elevation system and gravity reference system. In this paper, the surveying methods and the mathematical models for establishing these systems are discussed, and the accuracy of results is analysed.
