Simulation of dynamics of interacting rigid bodies including friction I: General problem and contact model

Abstract

This is the first of two papers that deal with the problem of modeling contact (impact, sliding, rolling) between unconstrained rigid bodies for computer simulation of their motion. Modeling impacts and sustained contact is difficult because of the lack of a concise theory for three-dimensional (3-D) impact with friction, the complex non-holonomic constraints involved, general complexity of friction, etc. The traditional rigid body ‘hard contact’ approach leads to a quadratic program formulation for determining the contact forces, which branches into cases and does not model multiple simultaneous contacts adequately. We have formulated a computational theory based on the ‘soft contact’ approach that models contact through localized non-permanent deformation in the vicinity of contact. The model of mechanical contact between polyhedral objects that we propose, strikes a balance between realism and computability. It is simple enough to permit numerical integration through periods of contact in reasonable time, yet rich enough to represent well a variety of contact behaviors. The main cost associated with our model is the need for small time steps during contact, which slows down the simulation. Starting with the motivation for our work, this paper describes the governing equations and constitutive laws for the interacting bodies. Issues pertaining to the solution approaches are then discussed. The final sections explain the mathematical details of our contact model. A companion paper [1] describes details of our computational theory and its integration into a software system.