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

This article is cited in 6 scientific papers (total in 6 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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    This publication is cited in the following articles:
    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, “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
    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
    5. 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
    6. R. G. Mukharlyamov, “Modelling of dynamics of mechanical systems with regard for constraint stabilization”, Fundamental and Applied Problems of Mechanics-2017, IOP Conference Series-Materials Science and Engineering, 468, IOP Publishing Ltd, 2018, 012041  crossref  isi  scopus
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