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Nelin. Dinam., 2013, Volume 9, Number 1, Pages 59–76 (Mi nd370)  

This article is cited in 14 scientific papers (total in 15 papers)

How to control the Chaplygin ball using rotors. II

Alexey V. Borisovabc, Alexander A. Kilinabc, Ivan S. Mamaevabc

a Institute of Computer Science; Laboratory of nonlinear analysis and the design of new types of vehicles, Udmurt State University, Izhevsk, Russia
b A. A. Blagonravov Mechanical Engineering Research Institute of RAS, Moscow, Russia
c Institute of Mathematics and Mechanics of the Ural Branch of RAS, Ekaterinburg, Russia

Abstract: In our earlier paper [2] we examined the problem of control of a balanced dynamically nonsymmetric sphere with rotors with no-slip condition at the point of contact. In this paper we investigate the controllability of a ball in the presence of friction. We also study the problem of the existence and stability of singular dissipation-free periodic solutions for a free ball in the presence of friction forces. The issues of constructive realization of the proposed algorithms are discussed.

Keywords: non-holonomic constraint, control, dry friction, viscous friction, stability, periodic solutions.

Full text: PDF file (2050 kB)
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UDC: 532.5
MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Received: 31.01.2013
Revised: 28.02.2013

Citation: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “How to control the Chaplygin ball using rotors. II”, Nelin. Dinam., 9:1 (2013), 59–76

Citation in format AMSBIB
\by Alexey~V.~Borisov, Alexander~A.~Kilin, Ivan~S.~Mamaev
\paper How to control the Chaplygin ball using rotors. II
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 1
\pages 59--76

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    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    2. T. B. Ivanova, E. N. Pivovarova, “Dinamika i upravlenie sfericheskim robotom s osesimmetrichnym mayatnikovym privodom”, Nelineinaya dinam., 9:3 (2013), 507–520  mathnet  crossref
    3. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    4. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara Chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754  mathnet
    5. A. A. Kilin, Yu. L. Karavaev, A. V. Klekovkin, “Kinematicheskaya model upravleniya vysokomanevrennym mobilnym sferorobotom s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 10:1 (2014), 113–126  mathnet
    6. T. B. Ivanova, E. N. Pivovarova, “Kommentarii k state A. V. Borisova, A. A. Kilina, I. S. Mamaeva Kak upravlyat sharom Chaplygina pri pomoschi rotorov. II”, Nelineinaya dinam., 10:1 (2014), 127–132  mathnet
    7. A. A. Kilin, Yu. L. Karavaev, “Kinematicheskaya model upravleniya sferorobotom s neuravnoveshennoi omnikolesnoi platformoi”, Nelineinaya dinam., 10:4 (2014), 497–511  mathnet
    8. A. P. Ivanov, “Ob upravlenii robotom-sharom pri pomoschi dvukh omnikoles”, Nelineinaya dinam., 11:2 (2015), 319–327  mathnet
    9. “Kommentarii nauchnogo redaktora”, Nelineinaya dinam., 11:2 (2015), 443–445  mathnet
    10. A. V. Borisov, Yu. L. Karavaev, I. S. Mamaev, N. N. Erdakova, T. B. Ivanova, V. V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541  mathnet  crossref
    11. V. V. Kozlov, “The dynamics of systems with servoconstraints. II”, Regular and Chaotic Dinamics, 20:4 (2015), 401–427  mathnet  crossref
    12. A. A. Kilin, E. V. Vetchanin, “Upravlenie dvizheniem tverdogo tela v zhidkosti s pomoschyu dvukh podvizhnykh mass”, Nelineinaya dinam., 11:4 (2015), 633–645  mathnet
    13. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    14. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    15. E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332  mathnet  crossref  crossref  mathscinet  isi  elib
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