Dynamic Analysis of 3D Multi Rigid Bodies with Discontinuous Velocities. (2nd Report). Application of Order-n Formulation.

This paper applies an order-n formulation, which efficiently solves dynamic equations of serial rigid body systems, to calculate the deployment process of a folded spacecraft model in space. A spacecraft model is considered to be free in space and has a tree topology with rigid multi-bodies. Discontinuities in velocity and angular velocity occur when a hinge is locked due to a ratchet mechanism during the deployment process. Equations between the velocity jump and the impulsive force are formulated in a recursive manner and are solved by using the order-n formulation. A numerical example demonstrates the validity of the present formulation. A center-arm and six panels of a spacecraft model are deployed due to the force of a shrunk spring.