The paper proposes a method aimed to performing numerical integration of the equations of motion for dynamic systems whose behavior experiences discontinuity. The involved discontinuity can be both acceleration discontinuity and velocity discontinuity. The method is based on a timely detection of discontinuity occurrences and on updating a state matrix for selection of the studied set of motion equations. Without loss of generality, the method is presented by referring to a single-degree-of-freedom system that undergoes Coulomb friction - static and kinetic - as well as instantaneous collisions. The reported results, obtained by a demonstrative PC program, show that both stick-slip phenomenon and characteristic impulsive dynamic behavior can be accurately predicted, even by reasonably large steps of integration, without numerical instability.
Managing discontinuity in dynamics / Innocenti, Carlo. - 63:(1994), pp. 37-42. (Intervento presentato al convegno Proceedings of the Energy-Sources Technology Conference tenutosi a New Orleans, LA, USA, nel 1994).
Managing discontinuity in dynamics
Innocenti Carlo
1994
Abstract
The paper proposes a method aimed to performing numerical integration of the equations of motion for dynamic systems whose behavior experiences discontinuity. The involved discontinuity can be both acceleration discontinuity and velocity discontinuity. The method is based on a timely detection of discontinuity occurrences and on updating a state matrix for selection of the studied set of motion equations. Without loss of generality, the method is presented by referring to a single-degree-of-freedom system that undergoes Coulomb friction - static and kinetic - as well as instantaneous collisions. The reported results, obtained by a demonstrative PC program, show that both stick-slip phenomenon and characteristic impulsive dynamic behavior can be accurately predicted, even by reasonably large steps of integration, without numerical instability.
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