Multiple impacts: A state transition diagram approach

Material for Multiple Impacts : A State Transition Diagram Approach

A State Transition Diagram for Simultaneous Collisions with Application in Billiard Shooting

This paper models a multibody collision in the impulse space as a state transition diagram, where each state represents a phase during which impacts are “active” at only a subset of the contact points. A state transition happens whenever an active impact finishes restitution, or an inactive impact gets reactivated, depending on whether the two involved bodies are instantaneously penetrating int...

Simultaneous Impacts: a State Transition Diagram Approach

Impact happens when two or more bodies collide, generating very large impulsive forces in a very short period of time during which kinetic energy is first absorbed and then released after some loss. This paper introduces a state transition diagram to model a frictionless multibody collision. Each state describes a different topology of the collision characterized by the set of instantaneously a...

UML Analysis Using State Diagrams

This article demonstrates a new approach to analyzing UML designs using state and sequence diagrams. From multiple state diagrams, a super-state diagram which includes the cross-product of the selected states is built along with a transition matrix of possible transitions. The closure of the transition matrix is used to identify unreachable states and impossible transitions. Additionally, the c...

Inconsistency Discovery in Multiple State Diagrams

In this article, we introduce a new approach for analyzing UML designs to detect the inconsistencies between multiple state diagrams and sequence diagrams. The Super State Analysis (SSA) identifies the inconsistencies in super states, single step transitions, and sequences. Because SSA considers multiple UML state diagrams, it discovers inconsistencies that cannot be discovered when considering...