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Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2014-6pp.568-579

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A.V. Vlakhova, "The dynamics of systems with rolling and gyroscopic systems with small generalized velocities and the realization of constraints," J. Appl. Math. Mech. 78 (6), 568-579 (2014)
Year 2014 Volume 78 Issue 6 Pages 568-579
Title The dynamics of systems with rolling and gyroscopic systems with small generalized velocities and the realization of constraints
Author(s) A.V. Vlakhova (Moscow, Russia, vlakhova@mail.ru)
Abstract Approaches to the construction of mathematical models of systems with rolling and gyroscopic systems with dynamics characterized by the smallness of some of the generalized velocities are discussed. As a rule, a quasistatic approach is used in the modelling of such systems, within the limits of which the generalized accelerations corresponding to small generalized velocities are assumed to be equal to zero. Cases are indicated when the possibility, established by Kozlov, of obtaining the quasistatic equations of gyroscopic systems by the imposition of holonomic constraints is extended to systems with rolling. Additional conditions are formulated that enable one to estimate the error in the quasistatic equations of systems with rolling and gyroscopic systems. It is shown that they can be refined with respect to a small parameter, that is, the ratio of the characteristic values of the "small" and "finite" generalized velocities, using the Dirac formalism, based on an analysis of the constraints between the generalized coordinates and momenta of the system that arise on account of the degeneracy of its Lagrangian on changing to the quasistatic equations.
Received 23 January 2014
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