1,721,052 research outputs found
First integrals and stability properties
No full textStability properties of equilibrium for a differential system satisfying a Lipschitz condition uniform on the time. Unconditional stability results are obtained when uniform asymptotic stability occurs with respect to the solutions for which a first integral assumes a fixed appropriate value. A complete discussion is given in a particular case frequently appearing in the applications
Conditional and unconditional stability properties of time dependent sets
No full textLet dx/dt = f(t,x) be a smooth differential equation in
R×R^n and M be an s--compact invariant set in Rx R^n. Assume the existence of a smooth invariant set Φ in
R×Rn containing M such that M is uniformly asymptotically stable with respect to the perturbations lying on Φ. We analyze the influence of the stability properties of Φ "near M" on the unconditional stability properties of M. A comparison with some classical results concerning the autonomous or the periodic case is also given
Time dependent forces and stability of equilibrium for holonomic systems
No full textThis paper concerns some results on stability of the equilibrium position of holonomic mechanical systems subject to a generalized conservative force and a dissipative one by means of families of Lyapunov functions. The most interesting results concern the case in which the generalized conservative force is the product of a conservative force and a function f(t) periodic in t. In this case we obtain asymptotic stability even if when there is instability for f(t)=1
First and invariant integrals in stability problems
No full textThe relationship between conditional and unconditional asymptotic stability properties of the null solution of a differential system satisfying a Lipschitz condition, uniform on the time, are considered. The conditional properties are given on an invariant manifold defined by a first integrals. The results are illustrated by their applications to a bifurcation problem
On the problem of total stability for periodic differential systems
No full textConsider a smooth ω-periodic differential system in
R×R^n, say S, of ordinary differential equations, and let E
be an equilibrium for S. Preliminarily it is shown that the total stability of E is equivalent to the existence of a fundamental family of asymptotically stable neighborhoods of E. Thus a known theorem of Seibert concerning autonomous systems is extended to periodic systems. Let us assume now the existence of a smooth
invariant manifold Φ in R×R^n, containing R×{E}, ω-periodic in t, and asymptotically stable near E. By using the above
extension of Seibert's theorem and some previous results in a previous paper of us, we prove here that if E is totally stable on Φ (that is with respect to the solutions lying on Φ), then E is unconditionally totally stable
Secular stability and total stability
No full textThis paper illustrates the problem of observability of phenomena for conservative systems in two different ways. By modifying the conservative schema and considering the influence of small dissipative forces neglected in a first approximation (asymptotic stability), or considering correct the conservative schema and requiring a stable behavior restricted to classes of perturbations of prevalent importance for the case under examination (conditional total stability)
First integrals and stability properties
No full textStability properties of equilibrium for a differential system satisfying a Lipschitz condition uniform on the time. Unconditional stability results are obtained when uniform asymptotic stability occurs with respect to the solutions for which a first integral assumes a fixed appropriate value. A complete discussion is given in a particular case frequently appearing in the applications
Su un concetto di stabilità totale assoluta.
No full textIn questo lavoro si mostra come la stabilità totale per un sistema dinamico autonomo possa essere definita tramite un opportuno prolungamento P (P-stabilità totale di ordine 0). Se per i successivi prolungamenti di qualunque ordine la proprietà continua a sussistere si parla di stabilità totale assoluta. È stato anche mostrato che la stabilità totale assoluta di un insieme compatto M rispetto al sistema dinamico è equivalente alla proprietà che M sia dotato di una famiglia fondamentale di intorni compatti asintoticamente stabili rispetto al sistema dinamico
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