Likhatchova V. Formation of triply orthogonal systems of surfaces and corresponding coordinate systems

An object is methods of construction of the triply ortogonal systems of surfaces and them analytical description. Aim - to systematize the structural schemes of formation of the triply ortogonal systems of surfaces; on their basis to enter the new triply ortogonal systems of coordinates; and also with the purpose of expansion of application domain to transform to triply ortogonal the oblique-angled curvilinear systems which are introduced for description of surfaces. Methods - synthetic at the level of development of structural schemes of formation of the triply ortogonal systems and analytical at the level of their introduction in science and practice. Novelty - the structural schemes of formation of the triply ortogonal systems of surfaces, suitable to realization are systematized; pursuant to structural schemes the general algorithms of drafting of functions which introduce the ortogonal systems of coordinates are worked out; regenerate in the ortogonal known oblique-angled systems of curvilinear coordinates on structural charts and analytical algorithms of their realization; worked out to recommendation on introduction of schemes of formation of the triply ortogonal systems and special ortogonal coordinations introduced on their basis in engineering practice. Results - analytical interpretation of the built triply ortogonal systems of surfaces as functions of introduction of ortogonal coordinations allows to choose coordination under an object, process or task, what is provide expansion of application of classic methods of analytical design on new objects, form and structure of which answer coordinate surfaces and coordinate lines of the chosen system. Domain of application is geometrical modeling in mechanical ingineering.