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Non-conservative positional systems - stability. (English) Zbl 0656.70028

The aim of the work is stability analysis of the system ẍ\(=F(x)\), \(x\in {\mathbb{R}}^ 2\), when the F(x) “force” is non-conservative. The necessary and sufficient condition for stability of the origin of the particular system ẍ\(=-xf(x)\), ÿ\(=-yf(x)\), \(x,y\in {\mathbb{R}}\), \(f(0)>0\) is examined and other interesting results are obtained. Some results are generalized for Lagrange’s equations. The paper is theoretical in character. It is addressed to the specialists working in the field of stability analysis of differential equations.
Reviewer: J.Wicher

MSC:

70K20 Stability for nonlinear problems in mechanics
34D20 Stability of solutions to ordinary differential equations
37C75 Stability theory for smooth dynamical systems
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References:

[1] Darboux M.G., Comptes Rendus, Academie des Sciences de Paris 84 pp 936– (1877)
[2] Halphen M., Comptes Rendus, Academie des Sciences de Paris 84 pp 939– (1877)
[3] Zampieri G., Dynamical Systems and Partial Differential Equations, Proceedings of the 7th ELAM pp 105– · Zbl 0638.35007
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