A hybrid scheme for simulation of planar rigid bodies with impacts and friction using impact mappings

• We present a method for numerical implementation of a hybrid system using an energetic impact law.
• We describe a hybrid scheme that allows for the simulation of impacting systems with chatter.
• We examine the dynamics of the planar rod system and discuss the role of friction in the system.
• We show how friction will reduce the rotational energy so that only symmetric motion will remain.

This paper introduces numerical techniques necessary for the implementation of impact maps derived from an energetic impact law for rigid-body impacts with friction at isolated contact points. In particular the work focuses on methodologies for long-term simulation with behaviours such as dynamic transitions and chatter. The methods are based on hybrid event-driven numerical solvers for ordinary differential equations together with system states to deal with the transitions. A slender rod impacting a periodically oscillating surface is used as an example to illustrate implementation and methods. The numerical scheme for the rod system is used to show how symmetry can play an important role in the presence of friction for long-term dynamics. This will show that surface oscillations with low frequencies tend to lead to periodic motions of the rod that are independent of friction. For higher frequencies however the periodic solutions are not that common and irregular motion ensues.