Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators

Mats Fredriksson (1) , Arne Nordmark (1)

1 KTH Solid Mechanics

The transition from stable periodic non-impacting motion to impacting motion is analysed for a mechanical oscillator. By using local methods, it is shown that a grazing impact leads to an almost one-dimensional stretching in state space. A condition can then be formulated, such that a grazing trajectory will be stable if the condition is fulfilled. If this is the case, the bifurcation will be continuous and the motion after the bifurcation can be understood by a one-dimensional mapping. This mapping is known to exhibit chaotic solutions as well as arbitrary long stable cycles, depending on parameters.

Domaines: Sciences de l'ingénieur [physics]

Mats Fredriksson, Arne Nordmark. Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1997, ⟨10.1098/rspa.1997.0069⟩. ⟨hal-01297285⟩