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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2013, Volume 9, Number 1, Pages 59–76 (Mi nd370)  
This article is cited in 15 scientific papers (total in 16 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
Full-text PDF (2050 kB) Citations (16)
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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.
Received: 31.01.2013
Revised: 28.02.2013
Document Type: Article
UDC: 532.5
MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Language: Russian
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
\Bibitem{BorKilMam13}
\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
\mathnet{http://mi.mathnet.ru/nd370}
Linking options:
  • https://www.mathnet.ru/eng/nd370
  • https://www.mathnet.ru/eng/nd/v9/i1/p59
    Cycle of papers Comments
    This publication is cited in the following 16 articles:
    1. E. A. Mityushov, N. E. Misyura, S. A. Berestova, “Kvaternionnaya model programmnogo upravleniya dvizheniem shara Chaplygina”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 408–421  mathnet  crossref
    2. 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
    3. A. P. Ivanov, “Ob upravlenii robotom-sharom pri pomoschi dvukh omnikoles”, Nelineinaya dinam., 11:2 (2015), 319–327  mathnet
    4. “Kommentarii nauchnogo redaktora”, Nelineinaya dinam., 11:2 (2015), 443–445  mathnet
    5. A. V. Borisov, Yu. L. Karavaev, I. S. Mamaev, N. N. Erdakova, T. B. Ivanova, V. V. Tarasov, “Eksperimentalnoe issledovanie dvizheniya tela s osesimmetrichnym osnovaniem, skolzyaschego po sherokhovatoi ploskosti”, Nelineinaya dinam., 11:3 (2015), 547–577  mathnet
    6. V. V. Kozlov, “Dinamika sistem s servosvyazyami. II”, Nelineinaya dinam., 11:3 (2015), 579–611  mathnet
    7. 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
    8. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    9. 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
    10. 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
    11. 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
    12. A. A. Kilin, Yu. L. Karavaev, “Kinematicheskaya model upravleniya sferorobotom s neuravnoveshennoi omnikolesnoi platformoi”, Nelineinaya dinam., 10:4 (2014), 497–511  mathnet
    13. 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
    14. T. B. Ivanova, E. N. Pivovarova, “Dinamika i upravlenie sfericheskim robotom s osesimmetrichnym mayatnikovym privodom”, Nelineinaya dinam., 9:3 (2013), 507–520  mathnet  crossref
    15. 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
    16. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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