A Computational Method for the Stability of a Class of Mechanical Systems

Authors: Barone-Netto A.¹; de Oliveira Cesar M.¹; Gorni G.²

Source: Journal of Differential Equations, Volume 184, Number 1, September 2002 , pp. 1-19(19)

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Abstract:

In this work, we obtain criteria for the stability of the origin for the systemPxuml;=-xf(x),&yuml;=-yg(x), where f,g are positive in a neighbourhood of 0 isin Ropf . We start with abstract necessary and sufficient conditions, and develop them into practical explicit conditions in terms of inequalities involving the successive derivatives of f(x), g(x) up to order 2 at x=0. Some examples are worked out. © 2002 Elsevier Science (USA).

Keywords: Lyapunov stability; Hill'; s equations; Mathieu'; s equations; Whittaker'; s equations; Sturm equations.

Language: English

Document Type: Research article

Affiliations: 1: Universidade de São Paulo, Caixa Postal 66 281, São, Paulo-SP, 05389-970, Brazil 2: Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 208, Udine, UD, I-33100, Italy

Publication date: 2002-09-01