title: Ð¡Ð¸Ð½ÑÐµÐ· Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÐµÑÐ¿Ð¸Ð»Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð»ÐµÑÐ°ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ 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: Synthesis of a dynamic model of an unmanned aerial vehicle
Creators: name: ÐÐ°Ð²ÑÑÐ»Ð¾Ð²Ð°, ÐÐ»Ð¸Ð·Ð°Ð²ÐµÑÐ°
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: 2024
Subjects: Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ
ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑ
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° Ð²ÑÐ¾ÑÐ¾Ð³Ð¾ ÑÐ¾Ð´Ð°
Python
Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹
Ð²ÐµÐºÑÐ¾ÑÐ½Ð¾-Ð¼Ð°ÑÑÐ¸ÑÐ½Ð°Ñ ÑÐ¾ÑÐ¼Ð°
Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ
ÑÐ¸Ð½ÑÐµÐ· ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ
mathematical model
quadcopter
Lagrange equation of the second kind
computer automation
vector-matrix form
information model
control synthesis

description: ÐÐ±ÑÐµÐºÑÐ¾Ð¼ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð»ÑÐµÑÑÑ Ð±ÐµÑÐ¿Ð¸Ð»Ð¾ÑÐ½ÑÐ¹ Ð»ÐµÑÐ°ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð¿Ð¿Ð°ÑÐ°Ñ â ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑ, ÐºÐ¾ÑÐ¾ÑÑÐ¹ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐµÑ ÑÐ¾Ð±Ð¾Ð¹ ÑÐ¸Ð¿ Ð²ÐµÑÑÐ¾Ð»ÐµÑÐ° Ð¸Ð»Ð¸ Ð¼ÑÐ»ÑÑÐ¸ÐºÐ¾Ð¿ÑÐµÑÐ°, Ð¾ÑÐ½Ð°ÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÑÑÑÐ¼Ñ Ð²Ð¸Ð½ÑÐ°Ð¼Ð¸. Ð ÑÐ°Ð±Ð¾ÑÐµ ÑÐ¸Ð½ÑÐµÐ·Ð¸ÑÑÐµÑÑÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÐ° Ð½Ð° Ð±Ð°Ð·Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° Ð²ÑÐ¾ÑÐ¾Ð³Ð¾ ÑÐ¾Ð´Ð°. ÐÐ»Ñ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð¹ Ð¿ÑÐ¾Ð²ÐµÑÐºÐ¸ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÐµÑÑÑ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ° SymPy Ð´Ð»Ñ ÑÐ·ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python. ÐÐµÐºÑÐ¾ÑÐ½Ð¾-Ð¼Ð°ÑÑÐ¸ÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ ÑÐ¸Ð½ÑÐµÐ·Ð¸ÑÐ¾Ð²Ð°ÑÑ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÑ ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÐ°. Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÐ° Ð½Ð° Ð±Ð°Ð·Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° Ð¸ ÑÐ¸Ð½ÑÐµÐ· Ð»Ð¾ÐºÐ°Ð»ÑÐ½Ð¾-Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼Ð¾Ð³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð½ÐµÐµ. ÐÐ»Ñ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ñ ÑÐµÐ»Ð¸ Ð½ÑÐ¶Ð½Ð¾ ÑÐµÑÐ¸ÑÑ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸: 1. ÐÐ·ÑÑÐ¸ÑÑ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÐ¾Ð²; 2. ÐÑÐ²ÐµÑÑÐ¸ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð´Ð»Ñ ÐÐÐÐ Ð½Ð° Ð±Ð°Ð·Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° Ð²ÑÐ¾ÑÐ¾Ð³Ð¾ ÑÐ¾Ð´Ð°; 3. Ð¡Ð¸Ð½ÑÐµÐ·Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð»Ð¾ÐºÐ°Ð»ÑÐ½Ð¾-Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼Ð¾Ðµ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð´Ð»Ñ Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð´Ð»Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÐ¸Ð½ÑÐµÐ·Ð¸ÑÐ¾Ð²Ð°Ð½ Ð¾Ð¿ÐµÑÐ°ÑÐ¾Ñ Ñ Ð¿ÑÐ¾ÐµÐºÑÐ¸Ð¾Ð½Ð½Ð¾-Ð¾Ð¿ÐµÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¹ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ ÑÐ²ÑÐ·ÑÑ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ñ ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ð¹ Ñ Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð¸ÑÐ¼Ð¸ Ð½Ð° Ð²ÐµÐºÑÐ¾ÑÑ ÑÐ°Ð·Ð¾Ð²ÑÑ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°Ñ Ð¸ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¹.
description: The object of the study is an unmanned aerial vehicle â a quadcopter, which is a type of helicopter or multicopter equipped with four propellers. The paper synthesizes a mathematical model of a quadcopter based on the Lagrange equation of the second kind. For effective verification of analytical transformations, the SymPy library for the Python programming language is used. The vector-matrix model allows you to synthesize control and explore the dynamics of a quadcopter. The aim of the work is to build a quadcopter model based on the Lagrange equation and synthesize locally acceptable control for it. To achieve this goal, you need to solve the following tasks: 1. Study the existing models of quadrocopters; 2. Derive a model for UAVs based on the Lagrange equation of the second kind; 3. Synthesize locally acceptable control for this model. As a result, an operator with projection-operator feedback has been synthesized for a dynamic system for the tasks of stabilizing program movements with restrictions on vectors of phase coordinates and controls.