title: ÐÐ¾Ð¼Ð±Ð¸Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸ÐµÐ¹ 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° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Combined spacecraft attitude control system
Creators: name: Ð¥ÑÑÑÑÐ°Ð»ÐµÐ², ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ
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: Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ñ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ¾Ð²
Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸
ÑÐµÐ°ÐºÑÐ¸Ð²Ð½Ð°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸
Ð»Ð¾ÐºÐ°Ð»ÑÐ½Ð¾ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÐµ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ
spacecraft attitude control
gravity-gradient stabilization
reaction control system
locally optimal control

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸ÐµÐ¹ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ°, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÐµÐ¹ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÑ Ð¸ ÑÐµÐ°ÐºÑÐ¸Ð²Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ: 1) ÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²ÐºÐ° Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸; 2) Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ Ð»Ð¾ÐºÐ°Ð»ÑÐ½Ð¾ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÑ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¹ ÑÐµÐ°ÐºÑÐ¸Ð²Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸; 3) ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¾ÑÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»ÑÐ½ÑÑ ÑÑÑÐ°Ð½Ð¾Ð²Ð¾Ðº ÑÐµÐ°ÐºÑÐ¸Ð²Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð¿ÑÐ¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ð¸ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ñ ÑÐµÐ»ÑÑ ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸Ð¸ ÑÐµÑÑÑÑÐ° ÑÐ°Ð±Ð¾ÑÐµÐ³Ð¾ ÑÐµÐ»Ð° Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»ÐµÐ¹. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ ÑÐ°Ð±Ð¾ÑÑ ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ñ Ð´Ð²Ð° Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð¸ Ð´Ð°Ð½Ñ ÑÐµÐºÐ¾Ð¼ÐµÐ½Ð´Ð°ÑÐ¸Ð¸ Ð¿Ð¾ Ð¸Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ. ÐÑÐ¸Ð¼ÐµÐ½ÑÐ½ Ð¿ÑÐ¾ÐµÐºÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÑ Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð½ÑÑ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¹ ÑÐµÐ°ÐºÑÐ¸Ð²Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ñ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐ¸ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° Ð¿Ð¾ Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð¸Ñ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ° Ð¿ÑÐ¸ Ð¾ÑÐºÐ»ÑÑÐµÐ½Ð¸Ð¸ ÑÐµÐ°ÐºÑÐ¸Ð²Ð½ÑÑ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»ÐµÐ¹ Ñ ÑÐµÐ»ÑÑ ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸Ð¸ ÑÐµÑÑÑÑÐ° Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»ÑÐ½ÑÑ ÑÑÑÐ°Ð½Ð¾Ð²Ð¾Ðº Ð¸ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ñ ÑÑÐ¾ÐºÐ° ÑÐ»ÑÐ¶Ð±Ñ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ°. Ð ÐµÐ·ÑÐ»ÑÑÐ°Ñ ÑÐ°Ð±Ð¾ÑÑ Ð¼Ð¾Ð¶Ð½Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ð¿ÑÐ¸ ÐºÐ¾Ð½ÑÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ¾Ð², Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÑÑÐ¸Ñ Ð³ÑÐ°Ð²Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð¼Ð¾Ð¼ÐµÐ½Ñ Ð² ÑÐ°Ð¼ÐºÐ°Ñ Ð¿Ð°ÑÑÐ¸Ð²Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÐ¸Ñ ÑÐµÐ°ÐºÑÐ¸Ð²Ð½ÑÐµ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»ÑÐ½ÑÐµ ÑÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð´Ð»Ñ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¿ÑÐ°Ð²Ð»ÑÑÑÐ¸Ñ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ð¹.
description: The given work is devoted to the development of a spacecraft attitude control system using gravity-gradient stabilization system and reaction control system. The research set the following goals: 1) derivation of sufficient conditions for the stability of the gravity-gradient stabilization system; 2) calculation of locally optimal controls for the reaction control system; 3) development of an algorithm for disabling thrusters when the conditions of stability of the gravity-gradient stabilization system are met to save the resource of the working mass of the thrusters. As a result of the work, two sufficient conditions for the stability of the gravity-gradient stabilization system are derived and recommendations for their application are given. The projection-operator method of solving the problem of quadratic functional conditional minimization is applied to calculate the locally optimal controls for the reaction control system. The ability of the gravitational moment to limit the rotation fluctuations of the spacecraft when thrusters are turned off is demonstrated. Therefore, the use of a gravity-gradient stabilization system reduces the consumption of the working mass of the thrusters. The result of the work can be used in the design of spacecraft using the gravity-gradient stabilization as a passive attitude control system and using thrusters to form control actions.