Stability of coupled oscillators
M. A. Guzev, A. A. Dmitriev
Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
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.
coupled oscillators, equilibrium, stability
PDF file (463 kB)
MSC: Primary 70E55; Secondary 70H12, 70H14
M. A. Guzev, A. A. Dmitriev, “Stability of coupled oscillators”, Dal'nevost. Mat. Zh., 15:2 (2015), 166–191
Citation in format AMSBIB
\by M.~A.~Guzev, A.~A.~Dmitriev
\paper Stability of coupled oscillators
\jour Dal'nevost. Mat. Zh.
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