On the Contact Duration Accuracy of Discrete-Time Collision Models

Vasileios Chatziioannou, Maarten van Walstijn

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Collisions are a vital part of the function of musical instruments. They occur in various forms and during different phases of oscillation, including transient and steady-state regimes. The non-smooth nature of the nonlinearity inherent to objects coming into contact and decoupling again poses several difficulties when it comes to formulating numerical models. Besides issues regarding numerical stability – that have recently been handled using energy methods – questions arise about how accurately different numerical schemes can approximate the trajectories of colliding objects. This paper presents a comparative analysis of two particular types of time-stepping algorithms (namely a two-point, two variable and a three-point, one-variable scheme) employed to simulate contact between a mass and a barrier. Focusing largely on cases for which the exact solution is known, the schemes are evaluated in terms of their ability to simulate the correct duration of contact.
Original languageEnglish
Title of host publicationThe 2017 International Symposium on Musical Acoustics (ISMA), Montreal: Proceedings
Number of pages4
Publication statusPublished - 18 Jun 2017


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