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Theor. Appl. Mech., 2019, Volume 46, Issue 1, Pages 1–14 (Mi tam1)  

On the dynamics of systems with one-sided non-integrable constraints

Valery V. Kozlov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: In the paper we take the first steps in studying the dynamics of systems with one-sided differential constraints defined by inequalities in the phase space. We give a general definition of motion for systems with such constraints. Within the framework of the classical non-holonomic model, and also for systems with servoconstraints (according to Béghin), we present the conditions under which the system leaves two-sided differential constraints. As an example, we consider the Chaplygin sleigh with a one-sided constraint, which is realized by means of an anisotropic force of viscous friction. Variational principles for the determination of motion of systems with one-sided differential constraints are presented.

Keywords: non-integrable constraints, servoconstraints, non-holonomic mechanics, vakonomic mechanics, one-sided constraint, unilateral constraint.

Funding Agency Grant Number
Russian Science Foundation 19-71-30012
The research was funded by a grant from the Russian Science Foundation (Project No. 19-71-30012).


DOI: https://doi.org/10.2298/TAM190123005K

Full text: PDF file (289 kB)

Bibliographic databases:

MSC: 70F25, 70H45
Received: 23.01.2019
Revised: 15.05.2019
Language:

Citation: Valery V. Kozlov, “On the dynamics of systems with one-sided non-integrable constraints”, Theor. Appl. Mech., 46:1 (2019), 1–14

Citation in format AMSBIB
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\by Valery V.~Kozlov
\paper On the dynamics of systems with one-sided non-integrable constraints
\jour Theor. Appl. Mech.
\yr 2019
\vol 46
\issue 1
\pages 1--14
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