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Nelin. Dinam., 2015, Volume 11, Number 3, Pages 579–611 (Mi nd495)  

This article is cited in 2 scientific papers (total in 2 papers)

Translated papers

The dynamics of systems with servoconstraints. II

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina st. 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 servo-constraint, 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


Full text: PDF file (516 kB)
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English version:
Regular and Chaotic Dinamics, 2015, 20:4, 401–427

UDC: 531.36
MSC: 70E18, 34C40
Received: 14.05.2015
Revised: 01.07.2015

Citation: V. V. Kozlov, “The dynamics of systems with servoconstraints. II”, Nelin. Dinam., 11:3 (2015), 579–611; Regular and Chaotic Dinamics, 20:4 (2015), 401–427

Citation in format AMSBIB
\Bibitem{Koz15}
\by V.~V.~Kozlov
\paper The dynamics of systems with servoconstraints. II
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 3
\pages 579--611
\mathnet{http://mi.mathnet.ru/nd495}
\transl
\jour Regular and Chaotic Dinamics
\yr 2015
\vol 20
\issue 4
\pages 401--427
\crossref{https://doi.org/10.1134/S1560354715040012}


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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, “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
  • Нелинейная динамика
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