Abstract
We consider conservative systems with gyroscopic forces and prove theorems on stability and instability of equilibrium states for such systems. These theorems can be regarded as a generalization of the Kelvin theorem to nonlinear systems.
Similar content being viewed by others
References
W. Thomson and P. Tait,Treatise on Natural Philosophy, Vol. 1, Clarendon Press, Oxford (1867).
N. G. Chetaev,Stability of Motion., Works on Analytical Mechanics [in Russian], Academy of Sciences of the USSR, Moscow(1962).
A. V. Karapetyan and V. V. Rumyantsev, “Stability of conservative and dissipative systems,” in:Results in Science and Technology.General Mechanics [in Russian], Vol. 6, VINITI (1983).
V. V. Rumyantsev and S. P. Sosnitskii, “On the instability of equilibrium states of holonomic conservative systems,”Prikl. Mat.Mekh.,57, Issue 6, 144–166 (1993).
D. R. Merkin,Gyroscopic Systems [in Russian], Nauka, Moscow 1974.
S. V. Bolotin and P. Negrini, “Asymptotic trajectories of gyroscopic systems,”Vestn. Most Univ., Ser. Mat. Mekh., No. 6, 66–75(1993).
V. V. Nemytskii and V. V. Stepanov,Qualitative Theory of Differential Equations [in Russian], Gostekhteoretizdat, Moscow-Leningrad 1949.
S. P. Sosnitskii, “On the stability of equilibrium state of natural systems,” in:Mathematical Simulation of Dynamical Processes inSystems of Bodies with Liquid [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988), pp. 38–43.
R. Courant,Partial Differential Equations, Interscience, New York 1962.
Rights and permissions
About this article
Cite this article
Sosnyts’kyi, S.P. On the gyroscopic stabilization of conservative systems. Ukr Math J 48, 1592–1599 (1996). https://doi.org/10.1007/BF02377826
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02377826