Abstract

Rigid body systems may undergo numerous types of dynamic interactions including collisions and continuous contact which considerably complicate systematic modelling and simulation of such problems. This thesis introduces a new modelling approach based on a hybrid system formulation to describe the dynamics of interacting rigid body systems. Interaction among physical objects occurs in two different forms: impulsive contact and continuous contact. Characteristics of impulsive and continuous contacts are different. Hence the modelling of each contact type requires the use of different approaches. While the impulse-modelling approach better simulates the impulsive contacts, our findings indicate that continues contact is much more accurately modeled using the sliding manifold method. The proposed hybrid system approach combines the impulse modelling method for collision interactions and the sliding manifold method to model the differential-algebraic equations associated with continuous contact interactions. Appropriate discrete states, events, reset maps, and threshold parameters that yield a hybrid automaton framework to describe interacting rigid body systems are developed. To illustrate the effectiveness of the proposed method a rolling ball simulation for a virtual reality system is presented.