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Regul. Chaotic Dyn., 2015, Volume 20, Issue 4, Pages 401–427 (Mi rcd3)  

This article is cited in 8 scientific papers (total in 8 papers)

The Dynamics of Systems with Servoconstraints. II

Valery V. Kozlov

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

Abstract: This paper addresses the dynamics of systems with servoconstraints where the constraints are realized by controlling the inertial properties of the system. Vakonomic systems are a particular case. Special attention is given to the motion on Lie groups with left-invariant kinetic energy and a left-invariant constraint. The presence of symmetries allows the dynamical equations to be reduced to a closed system of differential equations with quadratic right-hand sides. As the main example, we consider the rotation of a rigid body with a left-invariant servoconstraint, which implies that the projection of the body’s angular velocity on some body-fixed direction is zero.

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

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the grant of the Russian Scientific Foundation (project 14-50-00005).


DOI: https://doi.org/10.1134/S1560354715040012

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MSC: 70E18, 34C40
Received: 14.05.2015
Accepted:01.07.2015
Language:

Citation: Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. II”, Regul. Chaotic Dyn., 20:4 (2015), 401–427

Citation in format AMSBIB
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\by Valery V. Kozlov
\paper The Dynamics of Systems with Servoconstraints. II
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 4
\pages 401--427
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    1. 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
    2. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Istoriko-kriticheskii obzor razvitiya negolonomnoi mekhaniki: klassicheskii period”, Nelineinaya dinam., 12:3 (2016), 385–411  mathnet  crossref  zmath  elib
    3. 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
    4. 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
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    7. I. A. Bizyaev, V A. Borisov , V. V. Kozlov, I. S. Mamaev, “Fermi-like acceleration and power-law energy growth in nonholonomic systems”, Nonlinearity, 32:9 (2019), 3209–3233  crossref  mathscinet  zmath  isi  scopus
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