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 Regul. Chaotic Dyn., 2012, том 17, выпуск 3-4, страницы 234–242 (Mi rcd400)

On the Dynamics of a Rigid Body Carrying a Material Point

Anatoly P. Markeev

A. Yu. Ishlinsky Institute for Problems in Mechanics RAS, Vernadskogo 101, block 1, Moscow, 119526 Russia

Аннотация: In this paper we consider a system consisting of an outer rigid body (a shell) and an inner body (a material point) which moves according to a given law along a curve rigidly attached to the body. The motion occurs in a uniform field of gravity over a fixed absolutely smooth horizontal plane. During motion the shell may collide with the plane. The coefficient of restitution for an impact is supposed to be arbitrary. We present a derivation of equations describing both the free motion of the system over the plane and the instances where collisions with the plane occur. Several special solutions to the equations of motion are found, and their stability is investigated in some cases.
In the case of a dynamically symmetric body and a point moving along the symmetry axis according to an arbitrary law, a general solution to the equations of free motion of the body is found by quadratures. It generalizes the solution corresponding to the classical regular precession in Euler’s case.
It is shown that the translational motion of the shell in the free flight regime exists in a general case if the material point moves relative to the body according to the law of areas.

Ключевые слова: rigid body dynamics, collision, periodic motion, stability

 Финансовая поддержка Номер гранта Российский фонд фундаментальных исследований 11-01-00322 Министерство образования и науки Российской Федерации NSh - 4149.2012.111.G34.31.0039 This research was supported by the Russian Foundation for Basic Research (11-01-00322), the State Program for Support of Leading Scientific Schools (NSh - 4149.2012.1) and by the Grant of the Government of the Russian Federation for state support of scientific research conducted under supervision of leading scientists at Russian institutions of higher professional education (Contract No 11.G34.31.0039).

DOI: https://doi.org/10.1134/S1560354712030021

Реферативные базы данных:

Тип публикации: Статья
MSC: 70E55, 70F35, 70K42, 70E50
Поступила в редакцию: 19.03.2012
Принята в печать:25.03.2012
Язык публикации: английский

Образец цитирования: Anatoly P. Markeev, “On the Dynamics of a Rigid Body Carrying a Material Point”, Regul. Chaotic Dyn., 17:3-4 (2012), 234–242

Цитирование в формате AMSBIB
\RBibitem{Mar12} \by Anatoly P. Markeev \paper On the Dynamics of a Rigid Body Carrying a Material Point \jour Regul. Chaotic Dyn. \yr 2012 \vol 17 \issue 3-4 \pages 234--242 \mathnet{http://mi.mathnet.ru/rcd400} \crossref{https://doi.org/10.1134/S1560354712030021} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2956220} \zmath{https://zbmath.org/?q=an:1252.70025} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..234M} 

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