Numerical methods for a nonlinear impact model: A comparative study with closed-form corrections

Davide Rocchesso, Stefano Papetti, Davide Rocchesso, Federico Avanzini

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


A physically based impact modelalready known and exploited in the field of sound synthesis-is studied using both analytical tools and numerical simulations. It is shown that the Hamiltonian of a physical system composed of a mass impacting on a wall can be expressed analytically as a function of the mass velocity during contact. Moreover, an efficient and accurate approximation for the mass outbound velocity is presented, which allows to estimate the Hamiltonian at the end of the contact. Analytical results are then compared to numerical simulations obtained by discretizing the system with several numerical methods. It is shown that, for some regions of the parameter space, the trajectories of the discretized systems may significantly drift from the analytically derived curves. Two approaches, based on enforcing numerical energy consistency, are then proposed to improve the accuracy of numerical simulations
Original languageEnglish
Pages (from-to)2146-2158
Number of pages13
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering


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