Graph theoretic foundations of multibody dynamics

Dynamics of Multibody Systems: Conventional and Graph-Theoretic Approaches

Graph theoretic foundations of program slicing and integration

This paper generalizes program slicing algorithms originally defined over representations of programs to operate over directed graphs. Doing so provides a uniform framework to model Weiser’s and Ottenstein & Ottenstein’s approaches to program slicing as abstract mathematical operations transparent of any concerns of a program’s structure or its semantics. This transparency helps us in a) derivi...

Dynamics of Multibody Systems

Iterative Rigid Multibody Dynamics

The simulation of large rigid multibody systems is a challenge. Collisions and friction constraints cause non-smooth motions of the rigid bodies. Differential complementarity problems are therefore used to formulate the dynamical system. The efficient solution of such problems is difficult and the major focus of this thesis. Several modeling choices of varying accuracy and difficulty are presen...

Symbolic Lagrangian Multibody Dynamics

Symbolic Lagrangian formulations of the equations of motion of tree structured constrained mechanical systems have the potential to be both more efficient and more numerically robust than formulations which use nonlinear kinematic constraint equations. We derive a simple recursive factorization of the Lagrangian equations of motion which, along with our extended implementation of the D* symboli...