Geodesic
Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 4, pp. 533-542.

Voir la notice de l'article provenant de la source Math-Net.Ru

The motion of a piecewise linear oscillator is considered. It consists of two spring connected drawers on a conveyor belt moving at a constant speed. The equations of motion are averaged in one nonresonance case. A continuum of invariant tori is obtained that exists in the exact system. The attraction (in finite time) of the trajectories to the family of limit tori is proved (limit tori belong to the continuum of invariant tori). We also investigate zones of sticking, which cannot be detected by averaging.
Keywords: equations with discontinuities, piecewise linear oscillator, averaging method, sticking zone.
Mots-clés : invariant torus 
@article{ND_2017_13_4_a5,
     author = {A. E. Baikov and N. V. Kovalev},
     title = {Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator},
     journal = {Russian journal of nonlinear dynamics},
     pages = {533--542},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2017_13_4_a5/}
}
TY  - JOUR
AU  - A. E. Baikov
AU  - N. V. Kovalev
TI  - Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator
JO  - Russian journal of nonlinear dynamics
PY  - 2017
SP  - 533
EP  - 542
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2017_13_4_a5/
LA  - ru
ID  - ND_2017_13_4_a5
ER  - 
%0 Journal Article
%A A. E. Baikov
%A N. V. Kovalev
%T Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator
%J Russian journal of nonlinear dynamics
%D 2017
%P 533-542
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2017_13_4_a5/
%G ru
%F ND_2017_13_4_a5
A. E. Baikov; N. V. Kovalev. Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 4, pp. 533-542. http://geodesic.mathdoc.fr/item/ND_2017_13_4_a5/

[1] Andronov A. A., Vitt A. A., Khaikin S. E., Theory of oscillators, Pergamon Press, Oxford, 1966, 848 pp.

[2] Ivanov A. P., Fundamentals of the theory of systems with friction, R Dynamics, Institute of Computer Science, Izhevsk, 2011, 304 pp. (Russian)

[3] Filippov A. F., Differential equations with discontinuous righthand sides: Control systems, Math. Appl., 18, Springer, Dordrecht, 1988, X, 304 pp.

[4] Pascal M., Stepanov S., “Dynamics of coupled oscillators exited by dry friction”, Proceedings of 9th Conference on Dynamical Systems, Theory and Applications (December 17–20, 2007. Poland), 355–362