A single particle impact model for motion in avalanches
The authors investigate the global dynamics of a particle bouncing down a staircase. The steps of the staircase are rectangular (with sides of the length \(a\) and \(b\)) and the staircase itself is forward inclined over an angle \(\varphi\). It is assumed that the particle falls at least one step during its orbit, the other orbits being trivial. The particle has the initial conditions \(V=(u,v)\), its velocity, and the position \(z\). These three coordinates define the dynamical space. The dynamics of this model is described in dependence on the staircase inclination. In particular, it is proved that all periodic orbits of this system are attractors.
scientific article; zbMATH DE number 5612806