Special Coordinates Associated With Recursive Forward Dynamics Algorithm for Open Loop Rigid Multibody Systems

The recursive forward dynamics algorithm (RFDA) for a tree structured rigid multibody system has two stages. In the first stage, while going down the tree, certain equations are associated with each node. These equations are decoupled from the equations related to the node’s descendants. We refer them as the equations of RFDA of the node and the current paper derives them in a new way. In the new derivation, associated with each node, we recursively obtain the coordinates, which describe the system consisting of the node and all its descendants. The special property of these coordinates is that a portion of the equations of motion with respect to these coordinates is actually the equations of RFDA associated with the node. We first show the derivation for a two noded system and then extend to a general tree structure. Two examples are used to illustrate the derivation. While the derivation conclusively shows that equations of RFDA are part of equations of motion, it most importantly gives the associated coordinates and the left out portion of the equations of motion. These are significant insights into the RFDA.