title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð°ÐºÑÐ¾Ð±Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð², Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð½Ð° Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ð¸ ÑÐµÐ½Ð·Ð¾ÑÐ° Ð¸Ð½ÐµÑÑÐ¸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: Modelling of acrobatic elements based on the alteration of the moment of inertia
Creators: name: ÐÐ¸ÑÐ°Ð¹Ð»Ð¾Ð²Ð°, ÐÐ½Ð°ÑÑÐ°ÑÐ¸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: 2022
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÐÐ½ÐµÑÑÐ¸Ñ
ÐÑÐ°ÑÐµÐ½Ð¸Ðµ
Ð±Ð°Ð»Ð°Ð½Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ
Ð±Ð°Ð»Ð°Ð½Ñ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ°
conservation of linear momentum
conservation of angular momentum

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸ÐµÂ Ð°ÐºÑÐ¾Ð±Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð², Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð½Ð° Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ð¸ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸Â». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹Â Ð°ÐºÑÐ¾Ð±Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð², Ð²ÑÐ¿Ð¾Ð»Ð½ÑÐµÐ¼ÑÑ Ð·Ð° ÑÑÑÑ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐµÐ½Ð·Ð¾ÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸,Â Ð² ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸ Ð¿ÑÑÐ¶ÐºÐ¾Ð² Ð² Ð²Ð¾Ð´Ñ Ñ Ð²ÑÑÐºÐ¸ Ð¸ ÑÐ°Ð½ÑÐµÐ²Ð°Ð»ÑÐ½ÑÑ Ð²ÑÐ°ÑÐ°ÑÐµÐ»ÑÐ½ÑÑÂ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÐ°Ð²ÑÐ¸ÐµÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1) Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¿Ð¾ÑÐ¾Ð±Ð° Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐµÐ½Ð·Ð¾ÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð¿ÑÐ¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ð¸ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÐ¼ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð¸ ÐµÐ³Ð¾ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ; 2) ÑÐ¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ ÑÐ¿Ð¾ÑÑÑÐ¼ÐµÐ½Ð°; 3) ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹; 4) Ð°Ð½Ð°Ð»Ð¸Ð· Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ð¹ Ð² Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÑÂ ÑÑÐ»Ð¾Ð²Ð¸ÑÑ Ð½Ð° ÑÐµÑÐµÐ½Ð¸Ñ. Ð Ð°Ð±Ð¾ÑÐ° Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð° Ñ Ð¾Ð¿Ð¾ÑÐ¾Ð¹ Ð½Ð° Ð²Ð¸Ð´ÐµÐ¾Ð·Ð°Ð¿Ð¸ÑÐ¸ Ð²ÑÑÑÑÐ¿Ð»ÐµÐ½Ð¸Ð¹ ÑÐ¿Ð¾ÑÑÑÐ¼ÐµÐ½Ð¾Ð²Â Ð½Ð° ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐ¿Ð¾ÑÑÐ¸Ð²Ð½ÑÑ Ð¼ÐµÑÐ¾Ð¿ÑÐ¸ÑÑÐ¸ÑÑ, Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ Ð½Ð° Ð»ÐµÑÐ½Ð¸Ñ ÑÐ½Ð¾ÑÐµÑÐºÐ¸ÑÂ ÐÐ»Ð¸Ð¼Ð¿Ð¸Ð¹ÑÐºÐ¸Ñ Ð¸Ð³ÑÐ°Ñ 2018 Ð³Ð¾Ð´Ð°. Ð¡Ð¿Ð¾ÑÑÑÐ¼ÐµÐ½Ñ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ ÐºÐ°Ðº ÑÐ¸ÑÑÐµÐ¼ÑÂ ÑÐ²ÑÑÐ´ÑÑ ÑÐµÐ», Ð´Ð»Ñ ÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÑÑÑÑ Ð¸ ÑÐµÑÐ°ÑÑÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ.Â Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð­Ð¹Ð»ÐµÑÐ° Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð¿ÑÑÑÐ¼Â Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð² ÑÑÐµÐ´Ðµ MATLAB. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ð¹ Ð² Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÑÂ ÑÑÐ»Ð¾Ð²Ð¸ÑÑ Ð½Ð° ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ ÑÑÑÐ°Ð½Ð¾Ð²Ð¸ÑÑ ÑÐ²ÑÐ·Ñ Ð¼ÐµÐ¶Ð´ÑÂ ÑÑÐ¿ÐµÑÐ½Ð¾ÑÑÑÑ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÐ¼ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð¸ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÑÐ¼Ð¸Â Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ð¹ ÑÐ¿Ð¾ÑÑÑÐ¼ÐµÐ½Ð¾Ð² Ð¿ÑÐ¸ Ð¸Ñ Ð¸ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ð¸. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð³ÑÑÂ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð² ÑÑÐµÐ½Ð¸ÑÐ¾Ð²Ð¾ÑÐ½Ð¾Ð¼ Ð¿ÑÐ¾ÑÐµÑÑÐµ Ð´Ð»Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¸ ÐºÐ¾ÑÑÐµÐºÑÐ¸ÑÐ¾Ð²ÐºÐ¸Â Ð¸ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð¿Ð¾Ð´Ð¾Ð±Ð½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð².
description: The subject of the graduate qualification work is âModelling of acrobaticÂ elements based on the alteration of the moment of inertiaâ. This paper focuses on the creation of mathematical models of acrobaticÂ elements performed through the alteration of the inertia tensor, in particular divesÂ from a platform and turns in dancing. The research pursues the following goals: 1) the study of the methods of the inertia tensor alteration during theÂ performance of the elements in question and their mathematicalÂ description; 2) the formulation of the differential equations describing an athleteâsÂ motion; 3) numerical solution of the resulting equations; 4) the analysis of the influence of the modelâs parameters and initialÂ condition changes on the solution of the said equations. The work is based on video records featuring athletesâ performances atÂ diverse sporting events, including the 2018 Summer Youth Olympics. Athletes areÂ represented as rigid body systems, for whi ch equations of motion are formulatedÂ and solved. The numerical solutions are obtained by programming in MATLABÂ numeric computing environment. The study of the influence of the modelâs parameters and initial conditionÂ changes on the said solutions allows to establish relationships between a successfulÂ performance of the elements in question and the particularities of athletesâÂ movements during their performance. The results thus obtained might be used forÂ analysis and correction of the performance of such elements.