Open AccessCenter mass theorem in three dimensional spaces with constant curvature
Author(s) -
Ю. А. Курочкин,
Д. В. Шёлковый,
И. П. Боярина
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-3-328-334
Subject(s) - center of mass (relativistic) , center (category theory) , constant curvature , constant (computer programming) , mathematics , curvature , isotropy , mathematical analysis , space (punctuation) , metric (unit) , mean curvature , coordinate system , geometry , classical mechanics , physics , quantum mechanics , chemistry , operations management , energy–momentum relation , computer science , programming language , economics , crystallography , linguistics , philosophy
In this paper, based on the definition of the center of mass given in [1, 2], its immobility is postulated in spaces with a constant curvature, and the problem of two particles with an internal interaction, described by a potential depending on the distance between points on a three-dimensional sphere, is considered. This approach, justified by the absence of a principle similar to the Galileo principle on the one hand and the property of isotropy of space on the other, allows us to consider the problem in the map system for the center of mass. It automatically ensures dependence only on the relative variables of the considered points. The Hamilton – Jacobi equation of the problem is formulated, its solutions and the equations of trajectories are found. It is shown that the reduced mass of the system depends on the relative distance. Given this circumstance, a modified system metric is written out.