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Nelin. Dinam., 2012, Volume 8, Number 4, Pages 837–852 (Mi nd363)  

This article is cited in 2 scientific papers (total in 2 papers)

The problem of optimal control of a Chaplygin ball by internal rotors

Sergey V. Bolotin

Steklov Mathematical Institute of the Russian Academy of Sciences, Gubkina st. 8, Moscow, 119991, Russia

Abstract: We study the problem of optimal control of a Chaplygin ball on a plane by means of 3 internal rotors. Using Pontryagin maximum principle, the equations of extremals are reduced to Hamiltonian equations in group variables. For a spherically symmetric ball, the solutions can be expressed in by elliptic functions.

Keywords: nonholonomic constraint, vaconomic mechanics, optimal control, maximum principle, Hamiltonian

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
Russian Academy of Sciences - Federal Agency for Scientific Organizations


Full text: PDF file (286 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 531.36
MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Received: 04.09.2012
Revised: 09.11.2012

Citation: Sergey V. Bolotin, “The problem of optimal control of a Chaplygin ball by internal rotors”, Nelin. Dinam., 8:4 (2012), 837–852

Citation in format AMSBIB
\Bibitem{Bol12}
\by Sergey~V.~Bolotin
\paper The problem of optimal control of a Chaplygin ball by internal rotors
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 4
\pages 837--852
\mathnet{http://mi.mathnet.ru/nd363}


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    This publication is cited in the following articles:
    1. E. V. Vetchanin, I. S. Mamaev, “Optimal control of the motion of a helical body in a liquid using rotors”, Russ. J. Math. Phys., 24:3 (2017), 399–411  crossref  mathscinet  zmath  isi  scopus
    2. E. V. Vetchanin, A. A. Kilin, “Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body”, J. Dyn. Control Syst., 23:2 (2017), 435–458  crossref  mathscinet  zmath  isi  scopus
  • Нелинейная динамика
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