Constrained multibody systems: graph-theoretic Newton-Euler formulation

With the aid of graph theory it is possible to combine the topological information of a constrained rigid-body system with the mathematical formulation of the equations of motion in a direct, systematic, and consistent procedural fashion that lends itself to a straightforward computer implementation. Such a graph-theoretical formulation for the dynamics analysis and simulation of three-dimensional constrained rigid-body systems is presented. It is shown that through the graph-theoretic approach, the topological information contributes directly to the systematic formulation procedure and also to an efficient, directly implementable computer algorithm. This algorithm can be implemented in a recursive fashion that reduces the computational cost substantially. The main components of the numerical procedure can be traced back directly to the system graphs of the formulation phase with very little effort. The resulting system of differential equations is left in its implicit form and solved numerically