Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2011-3pp.258-268

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V.Yu. Ol'shanskii, "The quadratic integrals of a complex mechanical system in a permanent uniform field," J. Appl. Math. Mech. 75 (3), 258-268 (2011)
Year 2011 Volume 75 Issue 3 Pages 258-268
Title The quadratic integrals of a complex mechanical system in a permanent uniform field
Author(s) V.Yu. Ol'shanskii (Saratov, Russia, olshanskiy_vlad@mail.ru)
Abstract A mechanical system, consisting of an invariable rigid body (a carrier) and a subsystem, the configuration and composition of which may vary with time (the motion of its components with respect to the carrier is specified), is considered. The system moves in a uniform gravitational field around a fixed point of the carrier. The general form of the quadratic integral is obtained when there is no dynamic symmetry, and the necessary and sufficient conditions for it to exist are found. The conditions when the integral can be split into two independent integrals and the equations of motion are reduced to autonomous form, are obtained.
Received 03 June 2010
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