Regular and Chaotic Dynamics
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Regul. Chaotic Dyn., 1998, том 3, выпуск 1, страницы 66–76 (Mi rcd929)  

On motion of a rigid body about a fixed point with respect to a rotating frame

A. A. Burova, D. P. Chevallierb

a Calculational Center of The Russia Academy of Sciences, Vavilov str. 40, 117967 Moscow, Russia
b C.E.R.M.I.C.S. Ecole Nacionale des Ponts et Chaussees La Cortine, 93167 Noisy-le-Grand, France

Аннотация: It is well-known in the Theoretical Mechanics how using the Routh procedure one can reduce the order of the Lagrange equations describing the motion if the cyclic coordinates expressing the symmetry properties of the mechanical system are known [1], [2]. However, if the equations of motion are written in redundant variables then the procedure of reduction is not always obvious. The idea of the reduction for such systems can be traced back to Lyapunov (see [3], p. 353 -355), who proposed to consider a motion with respect to the rotating, in the general case nonuniformly, specially chosen frame in the problem on figures of equilibria of the rotating fluid. The development of the studies of Lyapunov was given in [4].
As it is known the general method of such reduction for equations of Poincaré–Chetayev was proposed by Chetayev [5], [6], see also [7]. However the realisation of the Chetayev's theorem on reduction is not always simple for real systems. In this paper the analogue of the Routh procedure is considered for the problem on motion of mechanical system consisting of the rigid body with the fixed point. The origine of the concept of the reduced (amended) potential is shown. The problem on motion of the affine-deformable body is considered in details.

DOI: https://doi.org/10.1070/RD1998v003n01ABEH000061


Реферативные базы данных:

Тип публикации: Статья
MSC: 70E15
Поступила в редакцию: 25.07.1997
Язык публикации: английский

Образец цитирования: A. A. Burov, D. P. Chevallier, “On motion of a rigid body about a fixed point with respect to a rotating frame”, Regul. Chaotic Dyn., 3:1 (1998), 66–76

Цитирование в формате AMSBIB
\RBibitem{BurChe98}
\by A. A. Burov, D.~P.~Chevallier
\paper On motion of a rigid body about a fixed point with respect to a rotating frame
\jour Regul. Chaotic Dyn.
\yr 1998
\vol 3
\issue 1
\pages 66--76
\mathnet{http://mi.mathnet.ru/rcd929}
\crossref{https://doi.org/10.1070/RD1998v003n01ABEH000061}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1652172}
\zmath{https://zbmath.org/?q=an:0927.70009}


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