Global recursive dynamics of articulated tree structures

Abstract

A rigorous global recursive formulation is developed for the dynamics of a classical articulated tree. The system in question is composed of rigid parts interconnected by spring loaded single hinges to form a tree. The global formulation addresses the dynamics of complete branches (subtrees). The external moments applied to the branch are brought to bear on the instantaneous moment of inertia of the branch. Corrections for deviations from rigidity are accumulated recursively from sub-branches. The translational motion is likewise treated by addressing the structure as a whole and accumulating effects of internal motion recursively. Global recursive dynamics is a rigorous reexpression of the equations of motion of the system in terms that are, at the same time, intuitive and directly computable. Applied sequentially, global recursive dynamics gives rise to a family of approximations, progressing from the rigid to the fully articulated, which converge to the solution as the time step tends to zero.