title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ñ Ð³ÑÐ°Ð²Ð¸ÑÐ¸ÑÑÑÑÐ¸Ñ ÑÐµÐ» Ñ ÑÑÑÑÐ¾Ð¼ Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð¾ Ð½ÐµÑÐ¿ÑÑÐ³Ð¸Ñ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ð¹
Creators: name: ÐÐ¸ÑÑÑÐ½, ÐÐ¼Ð¸ÑÑÐ¸Ð¹
name: ÐÐ¸ÑÑÑÐ½, ÐÐµÐ¾ÑÐ³Ð¸Ð¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2019
Subjects: ÐÑÐµÐ¼Ð¸ÑÐ½Ð¾Ðµ ÑÑÐ³Ð¾ÑÐµÐ½Ð¸Ðµ
ÐÐ°Ð»Ð°ÐºÑÐ¸ÐºÐ¸
ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ

description: Ð ÑÐ°Ð¼ÐºÐ°Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ñ ÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð³Ð¾ ÑÐ¸ÑÐ»Ð° Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÐµÐ», Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²ÑÑÑÐ¸Ñ
Ð¼ÐµÐ¶Ð´Ñ ÑÐ¾Ð±Ð¾Ð¹ ÑÐ¾Ð»ÑÐºÐ¾ Ð¿Ð¾ÑÑÐµÐ´ÑÑÐ²Ð¾Ð¼ Ð¿ÑÐ¸ÑÑÑÐµÐ¹ Ð¸Ð¼ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¸. Ð¦ÐµÐ»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ, ÑÑÐ¾ Ð²ÑÑÐ²Ð¸ÑÑ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ, ÑÐ°ÑÐ°ÐºÑÐµÑÐ½ÑÐµ ÑÐ°Ð·Ñ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÐµÐ», Ð¾Ð±ÑÐ°Ð·ÑÑÑÐ¸Ñ ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ðµ. Ð ÑÐ¾Ð´Ðµ ÑÐµÑÐµÐ½Ð¸Ñ Ð±ÑÐ»Ð° ÑÑÑÐµÐ½Ð°
Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ñ ÑÐµÐ», Ð¿ÑÐ¸ ÑÑÐ¾Ð¼ ÑÐ´Ð°Ñ ÑÑÐ¸ÑÐ°Ð»ÑÑ Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð¾ Ð½ÐµÑÐ¿ÑÑÐ³Ð¸Ð¼.
ÐÐ½ÐµÑÐ½Ð¸Ðµ, Ð¿Ð¾ Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ñ Ðº ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÐ¼Ð¾Ð¼Ñ ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ñ ÑÐµÐ», ÑÐ¸Ð»Ð¾Ð²ÑÐµ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð±ÑÐ»Ð¸ Ð¸ÑÐºÐ»ÑÑÐµÐ½Ñ. ÐÐ· Ð²ÑÐµÑ Ð²Ð½ÑÑÑÐµÐ½Ð½Ð¸Ñ ÑÐ¸Ð»Ð¾Ð²ÑÑ ÑÐ°ÐºÑÐ¾ÑÐ¾Ð², Ð´ÐµÐ¹ÑÑÐ²ÑÑÑÐ¸Ñ Ð² ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ð¸, ÑÑÑÐµÐ½Ð¾ ÑÐ¾Ð»ÑÐºÐ¾ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ðµ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ. Ð¡Ð¾Ð²Ð¾ÐºÑÐ¿Ð½Ð°Ñ Ð¼Ð°ÑÑÐ° Ð²ÑÐµÑ Ð³ÑÐ°Ð²Ð¸ÑÐ¸ÑÑÑÑÐ¸Ñ ÑÐµÐ» ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ñ Ð¾ÑÑÐ°ÑÑÑÑ Ð½ÐµÐ¸Ð·Ð¼ÐµÐ½Ð½Ð¾Ð¹ Ð½Ð° Ð¿ÑÐ¾ÑÑÐ¶ÐµÐ½Ð¸Ð¸ Ð²ÑÐµÐ¹ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸. Ð Ð°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°Ð»Ð°ÑÑ Ð·Ð°Ð´Ð°ÑÐ° ÐÐ¾ÑÐ¸ Ñ ÐµÑÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐ¼Ð¸ Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸
ÑÑÐ»Ð¾Ð²Ð¸ÑÐ¼Ð¸. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ ÐºÐ¾Ð½ÑÑÐ¾Ð»Ñ Ð·Ð° ÑÐ¾Ð´Ð¾Ð¼ ÑÐµÑÐµÐ½Ð¸Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð°ÑÑ, ÑÐ°Ðº Ð½Ð°Ð·ÑÐ²Ð°ÐµÐ¼Ð°Ñ, ÐºÑÐ¸Ð²Ð°Ñ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÐµÑ ÑÐµÐºÑÑÐµÐµ ÑÐ°Ð´Ð¸Ð°Ð»ÑÐ½Ð¾Ðµ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð¾ÑÐ±Ð¸ÑÐ°Ð»ÑÐ½ÑÑ ÑÐºÐ¾ÑÐ¾ÑÑÐµÐ¹ ÑÐµÐ» ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ñ. Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿Ð¾ÐºÐ°Ð·Ð°Ð», ÐºÐ°Ðº
Ð²Ð¸Ð´Ð¾Ð¸Ð·Ð¼ÐµÐ½ÑÐµÑÑÑ ÐºÑÐ¸Ð²Ð°Ñ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÑÐ½Ð¾Ð³Ð¾ ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ñ Ð²Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð¸ ÑÐ¾, ÑÑÐ¾
Ð³Ð¾ÑÐ¸Ð·Ð¾Ð½ÑÐ°Ð»ÑÐ½ÑÐ¹ ÑÑÐ°ÑÑÐ¾Ðº Ð½Ð° ÐºÑÐ¸Ð²Ð¾Ð¹ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ, ÑÑÐ¾ ÑÐ¾Ð»ÑÐºÐ¾ "Ð¼Ð³Ð½Ð¾Ð²ÐµÐ½Ð¸Ðµ" ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ ÑÐºÐ¾Ð¿Ð»ÐµÐ½Ð¸Ñ Ð³ÑÐ°Ð²Ð¸ÑÐ¸ÑÑÑÑÐ¸Ñ ÑÐµÐ». ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑ, ÑÑÐ¾, Ð¾ÑÑÐ°Ð²Ð°ÑÑÑ Ð² ÑÐ°Ð¼ÐºÐ°Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸, Ð¼Ñ Ð¿Ð¾Ð»ÑÑÐ°ÐµÐ¼ Ð²ÑÐµ Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¸ ÐºÑÐ¸Ð²ÑÑ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼ÑÑ Ð³Ð°Ð»Ð°ÐºÑÐ¸Ðº Ð±ÐµÐ· Ð¿ÑÐ¸Ð²Ð»ÐµÑÐµÐ½Ð¸Ñ Ð³Ð¸Ð¿Ð¾ÑÐµÐ·Ñ Ð¾ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½Ð¾ Ð½ÐµÐ½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼Ð¾Ð¹, Ð³ÑÐ°Ð²Ð¸ÑÐ¸ÑÑÑÑÐµÐ¹ "ÑÑÐ¼Ð½Ð¾Ð¹ Ð¼Ð°ÑÐµÑÐ¸Ð¸".
description: Numerical simulation of evolution of a cluster of a finite number of gravitating
bodies interacting only by their intrinsic gravity has been carried out. The goal of
the study was to reveal the main characteristic phases of the spatial distribution
of material bodies constituting the cluster. In solving the problem, the possibility of interbody collisions was taken into account, the collisions being assumed to
be absolutely inelastic. Forces external to the body cluster under consideration
were ignored. Among all the internal force factors acting within the cluster, only
the gravitational interaction was taken into account. The total mass of all the
gravitating bodies of the cluster was assumed to remain constant during the entire
evolution. The Cauchy problem with natural initial conditions was considered. To
check the process of solution, the so-called rotation curve was used which represents the current radial distribution of orbital velocities of the cluster bodies. The
numerical analysis showed time variations of the model cluster rotation curve and,
particularly, the fact that the rotation curve horizontal section is only a short moment in evolution of the gravitating bodies cluster. The results obtained within
the scope of classical mechanics show that it is possible to represent all the rotation
curve variations for the observed galaxies without appealing to the hypothesis of
non-observable gravitating âdark matterâ.