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

Russian Academy of Sciences
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2014-3pp.220-227

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I.N. Borisenko, T.Yu. Figurina, and F.L. Chernousko, "The quasistatic motions of a three-body system on a plane," J. Appl. Math. Mech. 78 (3), 220-227 (2014)
Year 2014 Volume 78 Issue 3 Pages 220-227
Title The quasistatic motions of a three-body system on a plane
Author(s) I.N. Borisenko (Moscow, Russia)
T.Yu. Figurina (Moscow, Russia,
F.L. Chernousko (Moscow, Russia)
Abstract A controlled three-body system on a horizontal plane with dry friction is considered. The interaction forces between each pair of bodies are controls that are not subject to prior constraints but must be chosen in such a way that the motions of the system generated by them are quasistatic, that is, the total force acting on each of the bodies must be close to zero. All motions in which one body moves and the other two are fixed are found in the class of quasistatic motions. The problem of the optimal displacement of a moving body between two specified positions on a plane such that the absolute magnitude of the work of the friction forces along the trajectory is a minimum is solved. The quasistatic controllability of a three-body system is demonstrated and algorithms for bringing it into a specified position are discussed. The system considered simulates a mobile robot consisting of three bodies between which control forces act that can be realized by linear motors. The sizes of the bodies are assumed to be negligibly small compared with the distances between them so that the bodies are treated as particles.
Received 30 September 2013
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