Concerning the geometric visualization of particle motion in space and time on the example of air traffic

DOI 10.51955/2312-1327_2021_1_6

Aleksandr P. Plyasovskikh

Abstract. The article presents a new original method of geometric visualization of particle (or aircraft) motion in space and time. The urgency of the proposed method stems from disadvantages of the traditional method of presenting the motion in space-time having as one of its coordinates the   time which is independent on spatial coordinates. In this space-time, the concept of distance between two points is not defined, the concepts of angle, triangle, geometric figures are not defined as well, it does not allow Euclidian geometry to be used. The author proposes the use of four-dimensional Euclidian space with the fourth axis z = bt where b is a speed constant, t is time, for presenting the motion of a particle (aircraft) in space and time. The particle (aircraft) motion presented with the use of the space proposed by the author is a visualized one, the track makes geometric sense of a Euclidian geometry line. The examples of presenting the four-dimensional motion of an aircraft along its route are given, the concept of four-dimensional corridor of aircraft motion is defined. It is shown that the proposed method could be used for description and research of particle (aircraft) motion in space and time. The method opens up a new direction of research of particles and other material objects moving in space and time with the use of multi-dimensional, in particular, four-dimensional geometry. The importance of the approach proposed in the article is that it opens new directions of scientific research in such sciences as physics (not relativistic mechanics), navigation and air traffic control, space mechanics and many other sciences in which processes of motion of different objects in space and time are researched. The author is going to continue publishing the results obtained due to the proposed method which are not included in the present paper because of space limitations.

Key words: air traffic control, 4D trajectory, 4D space, material particle, multidimensional geometry, space-time.

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