MATHEMATICAL METHODS IN GEOMATICS - EULER-URMAJEV SYSTEM OF EQUATIONS

M. Baranova

University of West Bohemia, Department of mathematics, Pilsen, Czech Republic

baranov@kma.zcu.cz

This doctoral thesis is being elaborated at Department of mathematics on Faculty of Applied sciences at the University of West Bohemia in Pilsen. This thesis is established/based on work of docent Pyšek, who was an excellent cartographer, specialized in mathematical cartography and who, as the first cartographer in the Czech Republic explained the theory of general approach of mathematical cartography. However his precocious death in 1995 let his work unfinished.

The main goal of presented work is to give detailed derivation and description of Euler-Urmajev system of equations as a system of differential equations of map projection in the most general expression. In the report will be explained the principle of equation system derivation, followed by its possible applications as well as its usage in the field of mathematical cartography. Those fields may be: optimalization of cartographical projections from the view-point of deformations, suggestion of possible sorting of all map projections, genetic classification of map projections and suggestion of process of derivation new map projections based on requirements of projection properties and desired behavior of deformations.

Part of the report should be a presentation of software, which solves not only Euler-Urmajev system of equations, but is also capable of solving other tasks of mathematical cartography.

In this report will be presented part of doctoral thesis called Mathematical methods in Geomatics. This thesis will be in the next year given to examination board for approbation.