Geodesic
Stability of coupled oscillators
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 166-191 
M. A. Guzev; A. A. Dmitriev. Stability of coupled oscillators. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 166-191. http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a2/
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     author = {M. A. Guzev and A. A. Dmitriev},
     title = {Stability of coupled oscillators},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {166--191},
     year = {2015},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study a system of two coupled oscillators and a modified system of these oscillators whose rods intersect and slide without friction relative to each other. The oscillators posed vertically in a uniform gravity field and its interaction is described by a potential depending on distance. We demonstrate that both systems have symmetrical and asymmetrical equilibrium states. Stability of the states depend on the interaction energy and distance between the oscillators' suspension centers. Stability regions for Hooke and Coulomb potentials are calculated in the parameter plane.

[10] Butikov E. I., “An improved criterion for Kapitza's pendulum stability”, J. Phys. A: Math. Theor., 44:29 (2011), 7–20 | DOI | MR

[11] Markeev A. P., “O dvizhenii svyazannykh mayatnikov”, Nelineinaya dinamika, 9:1 (2013), 27–38 | MR

[12] Tarasov B. G., Guzev M. A., “Mathematical Model of Fan-head Shear Rupture Mechanism”, Key Engineering Materials, 592:11 (2013), 121–124 | DOI

[13] Baboly M. G., Su M. F., Reinke C. M., Alaie S., Goettler D. F., El-Kady I., Leseman Z. C., “The effect of stiffness and mass on coupled oscillations in a phononic crystal”, AIP Advances, 3 (2013), 112121, 1–7 | DOI

[14] Lipfert J., Hao X., Dekker N. H., “Quantitative Modeling and Optimization of Magnetic Tweezers”, Biophysical Journal, 96:12 (2009), 5040–5049 | DOI