Periodic motion and bifurcations induced by the Painlevé paradox

Remco Leine (1) , Bernard Brogliato (2) , Henk Nijmeijer (1)

1 Department of Mechanical Engineering [Eindhoven]
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

In this paper we study the periodic motion and bifurcations of the Frictional Impact Oscillator, which consists of an object with normal and tangential degrees of freedom that comes in contact with a rigid surface. The Frictional Impact Oscillator contains the basic mechanism for a hopping phenomenon observed in many practical applications. We will show that the hopping or bouncing motion in this type of systems is closely related to the Painlevé paradox. A dynamical system exhibiting the Painlevé paradox has nonuniqueness and nonexistence of solutions in certain sliding modes. Furthermore, we will show that this type of systems can exhibit the Painlevé paradox for physically realistic values of the friction coefficient.

Mots clés: Contact; Linear complementarity problem; Nonuniqueness; Multibody dynamics

Domaines: Sciences de l'ingénieur [physics]

Remco Leine, Bernard Brogliato, Henk Nijmeijer. Periodic motion and bifurcations induced by the Painlevé paradox. European Journal of Mechanics - A/Solids, 2002, ⟨10.1016/S0997-7538(02)01231-7⟩. ⟨hal-01310673⟩