title: Ð£Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ Ñ Ð°Ð¾ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¾Ð¹ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Control of chaotic motion in a spacecraft
Creators: name: ÐÐ¾Ð»ÐµÑÐ½Ð¸ÐºÐ¾Ð²Ð°, ÐÐ»ÐµÐ½Ð°
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: 2023
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÐÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ðµ Ð»ÐµÑÐ°ÑÐµÐ»ÑÐ½ÑÐµ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÑ
Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐµ ÑÐ¸ÑÑÐµÐ¼Ñ
Ð¼ÐµÑÐ¾Ð´Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ
Ñ Ð°Ð¾ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ¶Ð¸Ð¼
nonlinear systems
control methods
chaotic motion

description: ÐÐ±ÑÐµÐºÑÐ¾Ð¼ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð»ÑÑÑÑÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ¾Ð². ÐÑÐµÐ´Ð¼ÐµÑÐ¾Ð¼ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð»ÑÑÑÑÑ Ð¼ÐµÑÐ¾Ð´Ñ Ð¿Ð¾Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ ÑÑÐ¸Ð»ÐµÐ½Ð¸Ñ ÑÐ°Ð¾ÑÐ°. Ð¦ÐµÐ»Ñ: Ð¸Ð·ÑÑÐ¸ÑÑ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ° Ð¸ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ°Ð¼Ð¸, ÑÐ¸Ð½ÑÐµÐ·Ð¸ÑÐ¾Ð²Ð°ÑÑ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð´Ð»Ñ Ð¿Ð¾Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ ÑÑÐ¸Ð»ÐµÐ½Ð¸Ñ ÑÐ°Ð¾ÑÐ° Ð² ÑÐ¸ÑÑÐµÐ¼Ðµ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÐ±Ð·Ð¾Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ¾Ð². 2. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð° Ð¿Ð¾Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ ÑÑÐ¸Ð»ÐµÐ½Ð¸Ñ ÑÐ°Ð¾ÑÐ° Ð² ÑÐ¸ÑÑÐµÐ¼Ð°Ñ. 3. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð½Ð° Ð¿ÑÐµÐ´Ð¼ÐµÑ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸. 4. Ð¡Ð¸Ð½ÑÐµÐ· ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð´Ð»Ñ ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ°Ð¾ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐµÐ¶Ð¸Ð¼Ð¾Ð². 5. Ð¡Ð¸Ð½ÑÐµÐ· ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð´Ð»Ñ ÑÐ°Ð¾ÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ. Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÑ, Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼ÑÐµ Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð³ÑÐ°ÑÐ¸ÐºÐ¾Ð² ÑÐ°Ð·Ð¾Ð²ÑÑ Ð¿Ð¾ÑÑÑÐµÑÐ¾Ð², Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ Ð¿Ð¾ÐºÐ°Ð·Ð°ÑÐµÐ»ÐµÐ¹ ÐÑÐ¿ÑÐ½Ð¾Ð²Ð° Ð¸ ÑÐ¸Ð½ÑÐµÐ· ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ ÑÐ²ÑÐ·Ð¸ Ð±ÑÐ»Ð¸ Ð¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ñ Ð² ÑÑÐµÐ´Ðµ MatLab. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¾ ÑÐ¸Ð½ÑÐµÐ·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¾ Ð´Ð²Ð° Ð²Ð¸Ð´Ð° ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ð¼ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ¾Ð¼: Ð¾Ð±ÐµÑÐ¿ÐµÑÐ¸Ð²ÑÐµÐµ Ð¿ÐµÑÐµÑÐ¾Ð´ Ð² ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ðµ Ð¸, Ð½Ð°Ð¾Ð±Ð¾ÑÐ¾Ñ, Ð²ÑÐ²Ð¾Ð´ÑÑÐµÐµ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ð¹ Ð°Ð¿Ð¿Ð°ÑÐ°Ñ Ð¸Ð· ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸.
description: The given work is devoted to studying equations of motion of spacecrafts and control of chaotic instability behavior in these systems. The purpose is to investigate existing mathematical models of spacecrafts and control methods, especially, control of chaotic instability. The research set the following goals: 1. Review of mathematical models of spacecrafts. 2. Exploration of control methods. 3. Study of the selected system for stability. 4. Stabilize the chaotic mode in a system. 5. Destabilize the selected stable system. The numerical experiments required for the study, the plotting of phase portraits, the calculation of Lyapunov exponents and the synthesis of feedback control were performed in MatLab. As a result of the work, the spacecraft control was successfully synthesized, which ensured the transition to a stable state and which, on the contrary, increased chaotic instability behavior of spacecraft.