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Nelin. Dinam., 2012, Volume 8, Number 2, Pages 219–229 (Mi nd318)  

This article is cited in 1 scientific paper (total in 1 paper)

On the dynamics of a rigid body carrying a material point

A. P. Markeev

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

Abstract: 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.

Keywords: rigid body dynamics, collision, periodic motion, stability

Full text: PDF file (358 kB)
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UDC: 531.36,531.38,531.66
MSC: 70E55,70F35,70K42,70E50
Received: 19.03.2012
Accepted:25.03.2012

Citation: A. P. Markeev, “On the dynamics of a rigid body carrying a material point”, Nelin. Dinam., 8:2 (2012), 219–229

Citation in format AMSBIB
\Bibitem{Mar12}
\by A.~P.~Markeev
\paper On the dynamics of a rigid body carrying a material point
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 2
\pages 219--229
\mathnet{http://mi.mathnet.ru/nd318}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Markeyev A.P., “Approximate Equations of Rotational Motion of a Rigid Body Carrying a Movable Point MASS”, Pmm-J. Appl. Math. Mech., 77:2 (2013), 137–144  crossref  mathscinet  zmath  isi  scopus
  • Нелинейная динамика
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