A system of inverted nonsmooth pendula: modelling an elderly person stepping over an obstacle

We derive a mechanical model of human motion where an elderly person decides to step over an obstacle rather than avoiding it. Such a decision may be deliberate or forced due to a sudden appearing obstacle in his/her way. The model is represented by a nonautonomous system of ordinary differential equations with discontinuous right hand side. We provide a notion of lateral stability. It is shown that increasing the angle between legs increases stability linearly. This implies that an individual reduces the risk of falling due to stepping over an obstacle by increasing the angle between legs.