| Absztrakt: | The authors study the following problem: a material point is
constrained to move on the surface $z-\lambda(t)(x\sp 2+y\sp
2)$ in a constant vertical field of gravity, with the friction
force $-\alpha(\dot x,\dot y,\dot z)=(-\alpha \dot x,-\alpha
\dot y,-\alpha \dot z)$, where $\lambda \in C\sp 2({\bbfR}\sb+,{\bbfR}\sb+)$
is decreasing and convex, $\alpha =const>0$. Sufficient conditions
on $\lambda$ and ${\ddot \lambda}$ are given for the stability
and instability of equilibrium $x=y=z=0$.}
\RV{Ju.Je.Gliklich |