We consider \ddot x=-x f(x), \ddot y=-y f(x) where f is continuous in a neighbourhood of 0 in the real line and f(0)>0. We find a necessary and sufficient condition for the stability of the origin. If f is even then we prove that the origin is stable if and only if f is locally constant at 0.
Attractive central forces may yield Liapunov instability
ZAMPIERI, Gaetano;
1986-01-01
Abstract
We consider \ddot x=-x f(x), \ddot y=-y f(x) where f is continuous in a neighbourhood of 0 in the real line and f(0)>0. We find a necessary and sufficient condition for the stability of the origin. If f is even then we prove that the origin is stable if and only if f is locally constant at 0.
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