6533b851fe1ef96bd12a900e
RESEARCH PRODUCT
Numerical methods for a nonlinear impact model: A comparative study with closed-form corrections
Davide RocchessoFederico AvanziniStefano Papettisubject
sound synthesis0209 industrial biotechnologyMathematical optimizationnumerical analysisaudio signal processingAcoustics and UltrasonicsDiscretizationComputer sciencePhysical system02 engineering and technologyParameter spaceEnergy conservationsymbols.namesake020901 industrial engineering & automation0202 electrical engineering electronic engineering information engineeringElectrical and Electronic EngineeringComputer simulationSettore INF/01 - Informaticasound synthesis; numerical analysis; audio signal processingNumerical analysisMathematical analysisphysics computing020207 software engineeringimpact modelingimpact soundsEnergy conservationNonlinear systemnumerical simulationsymbolsnonlinear dynamical systemHamiltonian (quantum mechanics)description
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 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-01 |