Euclidean space

Progress in astronomical measurements of the trajectories of the movement of celestial bodies reveals new effects that require justification. In particular, it refers to the slight drift of the Moon from the Earth. A solution to this problem is possible only based on an adequate mathematical model. To perform this, it was adapted Newton's law of universal gravitation to the case of moving masses in flat space and physical time. At the same time, the final speed of propagation of the gravitational field can be considered.

In astronomical research, the problem of measuring the trajectories of the gravitational maneuver of space vehi- cles in the gravitational field of large celestial bodies arises. The known measurement results differ from those predicted by classi- cal celestial mechanics. A practical solution to this anomaly is possible only based on an adequate mathematical model. For this purpose, we have adapted Newton’s law of universal gravitation to the case of moving masses in a possible range of speeds in flat space and physical time.

The Cauchy-Poisson method is extended to n-dimensional Euclidean space so that to obtain partial differential equations (PDEs) of a higher order.   The application in the construction of hyperbolic approximations is presented, generalizing and supplementing the previous investigations.   Restrictions on derivatives in Euclidean space are introduced.  The hyperbolic degeneracy by parameters and its realization in the form of necessary and sufficient conditions are considered.  As a particular case of 4-dimensional Euclidean space, keeping operators up to the 6th order, we obtain a generalize

Розглядаються питання щодо оптимізації геометричних засобів евклідового простору у методі скінченних елементів із залученням комп’ютерних засобів під час розрахунків деталей в середовищі CAD/CAE AutoCAD — Mechanical.