Coordinates in geodesy
著者
書誌事項
Coordinates in geodesy
Springer-Verlag, c1988
- : us
- : gw
- タイトル別名
-
Koordinaten auf geodätischen Bezugsflächen
大学図書館所蔵 全7件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Translation of: Koordinaten auf geodätischen Bezugsflächen
Bibliography: p. 242-244
Includes index
内容説明・目次
内容説明
In Coordinates in Geodesy definitions and transformations are treated based on the general principles of differential geometry for surfaces and three-dimensional Euclidean space, strictly using the tensor calculus. The broad approach applying general concepts of constructing and transforming coordinates allows clearly arranged solutions for all geodetic applications. Moreover, the great number of examples given in this book explain in detail the principles of coordinates in geodetic surveying using ellipsoids of revolution as reference surfaces.
目次
1. Introduction.- 2. General Fundamentals of Surface Coordinates.- 2.1 Fundamentals of the Theory of Surfaces.- 2.1.1 Rudiments.- 2.1.2 First Fundamental Form.- 2.1.3 Covariant and Contravariant Bases.- 2.1.4 Equations of Gauss and Weingarten.- 2.1.5 Covariant Derivatives of Surface Vectors.- 2.1.6 Measures of the Curvature of Surface Curves and Surfaces.- 2.1.7 Normal and Principal Curvatures of Surfaces.- 2.1.8 Surface Curves with Given Geodesic Curvature.- 2.1.9 Geodesic Lines.- 2.1.10 Geodesic Surface Coordinates.- 2.1.11 Special Studies of Geodesic Polar Coordinates.- 2.1.12 Riemannian Normal Coordinates.- 2.1.13 Isothermal Surface Coordinates.- 2.1.14 Special Studies of Isothermal Surface Coordinates.- 2.2 Fundamentals of Complex Analysis.- 2.2.1 Preliminary Remarks.- 2.2.2 Functions of a Complex Variable.- 2.2.3 Differentiation and Integration of Analytic Functions.- 2.2.4 Power Series of Analytic Functions.- 3. Representing the Transformation Equations Between Surface Coordinates by Power Series.- 3.1 Constructing Surface Coordinates.- 3.2 Representing Power Series.- 3.3 Transformations Between Geodesic Polar Coordinates and Arbitrary Surface Coordinates.- 3.3.1 General Transformation Equations.- 3.3.2 Calculating Small Geodesic Triangles.- 3.4 Transformations Between Geodesic Parallel Coordinates and Arbitrary Surface Coordinates.- 3.4.1 Indirect Representation by Power Series.- 3.4.2 Direct Representation by Power Series.- 3.5 Transformations Between Isothermal Surface Coordinates and Arbitrary Surface Coordinates.- 3.5.1 General Transformation Equations.- 3.5.2 Transformations Between Two Isothermal Coordinate Systems.- 4. Surface Coordinates on Ellipsoids of Revolution.- 4.1 Preliminary Remarks.- 4.2 Ellipsoids of Revolution and Their Representation Using Geographic Coordinates.- 4.3 Transformations Between Geodesic Polar Coordinates and Geographic Coordinates.- 4.3.1 Transforming the Coordinates.- 4.3.2 Transforming the Metric Tensor.- 4.3.3 Tangent Vectors and Azimuths of Geodesic r-Lines.- 4.3.4 Transformations Between the Arc Length of a Meridian and the Ellipsoidal Latitude.- 4.4 Transformations Between Soldner's Parallel Coordinates and Geographic Coordinates.- 4.4.1 Transforming the Coordinates.- 4.4.2 Transforming the Metric Tensor.- 4.4.3 Meridian Convergence.- 4.5 Defining Isothermal Surface Coordinates in the Geographic Coordinate System.- 4.6 Transformations Between Isothermal Geographic Coordinates and Geographic Coordinates.- 4.6.1 Preliminary Remarks.- 4.6.2 Isothermal Latitude.- 4.6.3 Isothermal Longitude.- 4.7 Transformations Between Gaussian Isothermal Coordinates and Geographic Coordinates.- 4.7.1 Directly Transforming the Coordinates.- 4.7.2 Indirectly Transforming the Coordinates.- 4.7.3 Transforming the Metric Tensor.- 4.7.4 Meridian Convergence.- 4.8 Transformations Between Gaussian Isothermal Coordinates and Geodesic Polar Coordinates.- 4.8.1 Directly Transforming the Coordinates.- 4.8.2 Tangent Vectors and Direction Angles of Geodesic r-Lines.- 4.8.3 Coordinate Transformation by Reducing Directions and Distances.- 4.9 Transformations Between Two Systems of Gaussian Isothermal Coordinates.- 4.9.1 Indirectly Transforming the Coordinates.- 4.9.2 Directly Transforming the Coordinates.- 4.10 Transformations Between Isothermal Stereographic Coordinates and Geographic Coordinates.- 4.10.1 Transforming the Coordinates.- 4.10.2 Transforming the Metric Tensor.- 5. Three-Dimensional Coordinates.- 5.1 Preliminary Remarks.- 5.2 Fundamentals of Three-Dimensional Euclidean Geometry.- 5.2.1 Coordinate Transformations.- 5.2.2 Representing Transformations Between Three-Dimensional Curvilinear and Cartesian Coordinates by Power Series.- 5.2.3 Space Curves.- 5.3 Surface-Normal Coordinates.- 5.3.1 General Fundamentals.- 5.3.2 Representing Transformations Between Surface-Normal Coordinates and Cartesian Coordinates by Power Series.- 5.3.3 Transformations Between Three-Dimensional Polar Coordinates and Polar Coordinates on the Reference Surface.- 5.4 Geodetic Coordinates.- 5.4.1 Preliminary Remarks.- 5.4.2 Geographically Geodetic Coordinates.- 5.4.3 Gaussian Geodetic Coordinates.- 5.4.4 Transformations Between Ellipsoidal Polar Coordinates and Polar Coordinates on the Reference Ellipsoid.- 5.5 Transformations Between Geographically Geodetic Coordinates.- 5.5.1 Fundamentals.- 5.5.2 Transformations Between Concentrically Geodetic Coordinate Systems.- 5.5.3 Transformations Between Arbitrary Geodetic Systems Based on Central Transformation Parameters.- 5.5.4 Transformations Between Arbitrary Geodetic Systems Based on Local Transformation Parameters.- 5.5.5 Determining Transformation Parameters.- 5.5.6 Determining Mean Reference Ellipsoids.
「Nielsen BookData」 より