The authors consider the problem of the stability of the origin for x¨+xf(x)=0, y¨+yw(x)=0, (x,y)∈R2, f(0)>0. The aim of this paper is (a) to establish some wide collections of problems related to the coexistence of solutions of certain families of Hill's equations (for example, one of them is obtained with w=f), and (b) to determine all the cases which admit a first integral V quadratic in the velocities, and to solve the relative problems in stability of the equilibrium whenever V is a Lyapunov function.
On Liapunov stability for x¨+xf(x)=0, y¨+yw(x)=0
ZAMPIERI, Gaetano
1988-01-01
Abstract
The authors consider the problem of the stability of the origin for x¨+xf(x)=0, y¨+yw(x)=0, (x,y)∈R2, f(0)>0. The aim of this paper is (a) to establish some wide collections of problems related to the coexistence of solutions of certain families of Hill's equations (for example, one of them is obtained with w=f), and (b) to determine all the cases which admit a first integral V quadratic in the velocities, and to solve the relative problems in stability of the equilibrium whenever V is a Lyapunov function.
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