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Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 205–224 (Mi rcd1)  

This article is cited in 10 scientific papers (total in 10 papers)

The Dynamics of Systems with Servoconstraints. I

Valery V. Kozlov

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

Abstract: The paper discusses the dynamics of systems with Béghin's servoconstraints where the constraints are realized by means of controlled forces. Classical nonholonomic systems are an important particular case. Special attention is given to the study of motion on Lie groups with left-invariant kinetic energy and left-invariant constraints. The presence of symmetries allows one to reduce the dynamic equations to a closed system of differential equations with quadratic right-hand sides on a Lie algebra. Examples are given which include the rotation of a rigid body with a left-invariant servoconstraint the projection of the angular velocity onto some direction fixed in the body is equal to zero (a generalization of the nonholonomic Suslov problem) and the motion of the Chaplygin sleigh with servoconstraints of a certain type. The dynamics of systems with Béghin's servoconstraints is richer and more varied than the more usual dynamics of nonholonomic systems.

Keywords: servoconstraints, symmetries, Lie groups, left-invariant constraints, systems with quadratic right-hand sides.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
The study was financed by the grant from the Russian Science Foundation (Project No. 14-5000005).


DOI: https://doi.org/10.1134/S1560354715030016

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 34D20, 70F25, 70Q05
Received: 10.02.2015
Accepted:05.03.2015
Language: English

Citation: Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. I”, Regul. Chaotic Dyn., 20:3 (2015), 205–224

Citation in format AMSBIB
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\paper The Dynamics of Systems with Servoconstraints. I
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    This publication is cited in the following articles:
    1. Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. II”, Regul. Chaotic Dyn., 20:4 (2015), 401–427  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    2. V. P. Pavlov, V. M. Sergeev, “Fluid dynamics and thermodynamics as a unified field theory”, Proc. Steklov Inst. Math., 294 (2016), 222–232  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Historical and critical review of the development of nonholonomic mechanics: the classical period”, Regular and Chaotic Dynamics, 21:4 (2016), 455–476  mathnet  crossref  crossref  zmath  elib
    4. S. Celikovsky, M. Anderle, “Hybrid invariance of the collocated virtual holonomic constraints and its application in underactuated walking”, IFAC-PapersOnLine, 49:18 (2016), 802–807  crossref  mathscinet  isi  scopus
    5. S. Celikovsky, M. Anderle, “On the collocated virtual holonomic constraints in Lagrangian systems”, Proceedings of the American Control Conference, 2016 American Control Conference (ACC), IEEE, 2016, 6030–6035  crossref  isi
    6. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. H. Kang, C. Liu, Ya.-B. Jia, “Inverse dynamics and energy optimal trajectories for a wheeled mobile robot”, Int. J. Mech. Sci., 134 (2017), 576–588  crossref  isi  scopus
    8. N. S. Sevryugina, M. A. Stepanov, “Vertical transport: resource by the criterion of safety”, Mag. Civ. Eng., 75:7 (2017), 23–36  crossref  isi  scopus
    9. S. Celikovsky, M. Anderle, “Collocated virtual holonomic constraints in Hamiltonian formalism and their application in the underactuated walking”, 2017 11Th Asian Control Conference (ASCC), IEEE, 2017, 192–197  crossref  isi
    10. B. I. Adamov, “A Study of the Controlled Motion of a Four-wheeled Mecanum Platform”, Nelineinaya dinam., 14:2 (2018), 265–290  mathnet  crossref  elib
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