Development of Methods of Analytical Geometry of a Sphere for Solving Geodesy and Navigation Tasks // Zapiski Gornogo instituta. Key words: sphere, analytical geometry, inner geometry, elliptical plane, Riemann geometry, Cartesian ordi-nates, polar coordinates, tangential coordinates It also introduces several formulas for primary, secondary and higher-order curves for this sphere. The article describes main formulas of analytical geometry for projected elliptical plane, which correspond to geometry of projected sphere. With the help of central projection of sphere points on tangential plane the corresponding elliptical plane with beltrami ordinates was introduced. The Cartesian ordinates were introduced into the sphere and the relation between them and polar spherical coordinates was established. It was proved that spherical hyperbola and parabola are spherical ellipses with specific parameters.
It examines peculiarities of sphere inner geometry and properties of its primary, secondary and higher-order curves. The article develops ideas and formulas of analytical geometry for spherical surface of the Earth globe in relation to main tasks of global geodesy and navigation. Saint-Petersburg Mining University, Saint-Petersburg, Russia KhudyakovĝOI: 10.18454/PMI.2017.1.70ĭevelopment of Methods of Analytical Geometry.ĭEVELOPMENT OF METHODS OF ANALYTICAL GEOMETRY OF A SPHERE FOR SOLVING GEODESY AND NAVIGATION TASKS
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