Periodic motion and bifurcations induced by the Painlevé paradox. (English) Zbl 1023.70009
Summary: We study the periodic motion and bifurcations of 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 show that the hopping or bouncing motion in this type of systems is closely related to Painlevé paradox. A dynamical system exhibiting the Painlevé paradox has nonuniqueness and nonexistence of solutions in certain sliding modes. Furthermore, we show that this type of systems can exhibit Painlevé paradox for physically realistic values of friction coefficient.
MSC:
| 70K42 | Equilibria and periodic trajectories for nonlinear problems in mechanics |
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
| 70F40 | Problems involving a system of particles with friction |
Keywords:
nonuniqueness; multibody dynamics; linear complementarity problem; contact; periodic motion; bifurcations; frictional impact oscillator; hopping phenomenon; Painlevé paradox; nonexistence of solutions; friction coefficientReferences:
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