ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Neimark Y. I., Smirnova V. N. Paradox of painleve and auto-oscillation with coulomb friction. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 6, pp. 102-108. DOI: 10.18500/0869-6632-2002-10-6-102-108

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2002no6p102.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Article
UDC: 
517.958:539.3
DOI: 
10.18500/0869-6632-2002-10-6-102-108

Paradox of painleve and auto-oscillation with coulomb friction

Autors: 
Neimark Yurij Isaakovich, Lobachevsky State University of Nizhny Novgorod
Smirnova Vera Nikolaevna, Lobachevsky State University of Nizhny Novgorod
Abstract: 

There was discovered the possibility of auto-oscillation in mechanical systems with Painleve paradox in spite of the friction characteristic incident section absense.

Key words: 
-
Acknowledgments: 
The work was supported by the Russian Ministry of Education, grant Е00-1-109.
Reference: 

1. Painlevé P. Leçons sur le frottement. Hachette Livre; 1895. 120 p. (in French).
2. Neimark YI, Smirnova VN. Idealization, mathematical modeling and the Painlevé paradox. Bulletin of Nizhny Novgorod State University. Mathematical Modeling and Optimal Control. 1999;2:536 (in Russian).
3. Vasil'eva AB. Contrasting structures in systems of singularly perturbed equations. Comput. Math. Math. Phys. 1994;34(8–9):1007–1017.
4. Neimark YI, Smirnova VN. Singularly perturbed problems and the Painlevé paradox. Diff. Equat. 2000;36(11):1639–1646. DOI: 10.1007/BF02757365.
5. Butenin NV. Consideration of “degenerate” dynamical systems using the “jump” hypothesis. Journal of Applied Mathematics and Mechanics. 1948;12(1):3–22 (in Russian).
6. An LS. The painleve paradoxes and the law of motion of mechanical systems with Coulomb friction. Journal of Applied Mathematics and Mechanics. 1990;54(4):430–438. DOI: 10.1016/0021-8928(90)90052-C.
7. Fufaev NA. System dynamics in the Painlevé-Klein example: on the Painlevé paradox. Mechanics of Solids. 1991;(4):48–53 (in Russian).
8. Neimark YI. Once again about the Painlevé paradox. Mechanics of Solids. 1995;(1):17-21 (in Russian).
9. Neimark YI, Fufayev NA. The Painlevé paradoxes and the dynamics of a brake shoe. Journal of Applied Mathematics and Mechanics. 1995;59(3):343–352. DOI: 10.1016/0021-8928(95)00041-M.
10. Neimark YI, Smirnova VN. Contrast structures, limit dynamics, and the Painlevé paradox. Diff. Equat. 2001;37(11):1580–1588. DOI: 10.1023/A:1017916832078.
11. Neimark YI, Smirnova VN. On the influence of viscous friction on the dynamics of the Painlevé-Klein system. In: Abstracts of the V International Conference “Nonlinear Oscillations of Mechanical Systems”. Nizhny Novgorod; 1999. P. 165 (in Russian).
12. Neimark YI, Smirnova VN. To the centenary of the problem of the Painlevé paradox. Bulletin of the Nizhny Novgorod State University. Mathematical Modeling and Optimal Control. 2001;(2):7–33 (in Russian).

Received: 
14.06.2001
Accepted: 
15.01.2002
Published: 
10.02.2003
  • 467 reads