 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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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 |
| Link to Fulltext |
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