An efficient dynamic formulation for multibody systems

The objective of this article is to present an efficient extension of Rosen thal's order-n algorithm to multibody systems containing closed loops. The equations of motion are created by using relative coordinates and partial v elocity theory. Closed topological loops are handled by cut joint technique . The set of constraint equations of cut joints is adjoined to the system's equation of motion by using Lagrange multipliers. This results in the equa tion of motion as a differential-algebraic equation (DAE) rather than an or dinary differential equation. This DAE is then solved by applying the exten ded Rosenthal's order-n algorithm proposed in this article. While solving D AE, violation of the kinematic constraint equations of cut joints is correc ted by coordinate projection method. Some numerical simulations are carried out to demonstrate efficiency of the proposed method.