An explicit scheme for energy-stable simulation of mass-barrier collisions with contact damping and dry friction

Collisions feature in the acoustics of many musical instruments, and as such need to be included in physical models that aim to capture the resulting dynamics. Previous studies have established various ways of constructing energy-stable schemes for numerical modelling of collisions, usually in implicit form. Recent methods use energy quadratisation in the derivation of explicit update forms, which are particularly useful in a real-time synthesis context. This approach is extended here by including contact damping and sliding friction in a 2D one-mass impact oscillator model, which serves as an initial testbed problem. The scheme's guaranteed passivity is formally shown, and brief simulation and convergence results are included.