Extension of the Center Manifold Approach, Using Rational Fractional Approximants, Applied to Non-Linear Stability Analysis

Jean-Jacques Sinou (1) , Fabrice Thouverez (1) , Louis Jezequel (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

A method is presented which extends the domain of the validity of non-linear systems reduced by using the centermanifold approach. This methodology applies rational fractional approximants in order to enhance the convergence ofthe series expansions of the center manifold theory.Effectively, a sequence of rational fractional approximantsmay converge even if the associated series does not; one canthen extend the domain of convergence. In this study, thedomain of validity of the solution is successfully enhanced byemploying rational fractional approximants. Here the basic ideas are outlined, an example ispresented, and some natural extensions and possibleapplications of this methodology are briefly described in the conclusions.

Mots clés: center manifold theory; rational approximants; extension of the domain of validity; non-linear analysis

Domaines: Mécanique [physics.med-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

Jean-Jacques Sinou, Fabrice Thouverez, Louis Jezequel. Extension of the Center Manifold Approach, Using Rational Fractional Approximants, Applied to Non-Linear Stability Analysis. Nonlinear Dynamics, 2003, 33, pp.267-282. ⟨10.1023/A:1026060404109⟩. ⟨hal-00322922⟩