Abstract
We discuss the conjecture that an isolated equilibrium of a mechanical system in a solenoidal force field is unstable. A number of statements confirming this conjecture under additional general position conditions guaranteeing that the equilibrium is isolated are proved. More precisely, we prove that there exist phase trajectories asymptotically leaving the equilibrium state.
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Funding
This work was supported by the Russian Science Foundation under grant 21-71-30011.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 207–216 https://doi.org/10.4213/mzm13884.
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Kozlov, V.V. Instability of Equilibria in a Solenoidal Force Field. Math Notes 113, 220–227 (2023). https://doi.org/10.1134/S000143462301025X
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DOI: https://doi.org/10.1134/S000143462301025X