Summary: 2146 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 19, NO. 7, SEPTEMBER 2011
Numerical Methods for a Nonlinear Impact Model: A
Comparative Study With Closed-Form Corrections
Stefano Papetti, Federico Avanzini, and Davide Rocchesso
Abstract--A physically based impact model--already 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 ap-
proximation 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 ob-
tained by discretizing the system with several numerical methods.
It is shown that, for some regions of the parameter space, the tra-
jectories 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.
Index Terms--Energy conservation, impact modeling, nonlinear