Sull'esistenza globale in futuro e sulla limitatezza parziale dei moti di un'ampia classe di sistemi olonomi scleronomi

Sufficient conditions for the global existence in the future and the partial boundedness of the motions of a wide class of holonomic scleronomic systems are given, using the comparison method introduced by R. Conti [4], and taking as Liapunov function the total energy of the system. The theorems obtained in the present paper can be used both when the potential energy of the system is bounded from below (a case studied by the second author [8], [3]) and when it is not (a case first studied by G. Cantarelli [1], [2], and independently by P. Pucci and J. Serrin [7])

The comparison method applied to the stability of systems with known first integrals

Using the comparison method, the stability study of the unperturbed motion of a differential system of /b n/ scalar equations with /b m/ known independent first integrals (1<or=/b m/</b n /), is reduced to that of the corresponding solution of a certain reduced system of 8/b n/-/b m/) scalar equations. Some theorems of stability and partial asymptotic stability of the unperturbed motion are given. These results are applied in Mechanics for the stability study of generalized steady motions of non-autonomous holonomic dissipative systems with ignorable coordinates. As an illustration, a concrete example of a stabilization problem by means of an elastic force with time-varying coefficient is given.Anglai

Global existence in the future and partial boundedness of motions of a wide class of scleronomic holonomic systems

Sufficient conditions for the global existence in the future and the partial boundedness of the motions of a wide class of holonomic scleronomic systems are given, using the comparison method introduced by Conti [4], and taking as Liapunov function the total energy of the system, in the case a)when the potential energy is bounded from belov and b)when it is not