Open Multibody Systems

In open multibody systems, the joint coordinates are also minimal coordinates. Open multibody systems with holonomic joints. are considered here. The equations of motion are conveniently set up as ordinary differential equations in the joint coordinates, as the explicit constraints can be directly formulated in analytical form, i.e., without first setting up the implicit constraints, at least for revolute and prismatic joints and joints composed of these. Based on the topological description of the tree structure using topology matrices, the explicit constraints of the individual bodies are formulated using the explicit constraints of the joints. The constraints at the acceleration level, together with the implicit constraint reaction conditions and the linear and angular momentum laws of the bodies, form the system of linear equations for the absolute accelerations of the bodies, the joint accelerations, and the constraint wrenches. It provides the common approach to the non-recursive and recursive formalisms for setting up the equations of motion in the minimal coordinates.