An efficient dynamic formulation for multibody systems

The objective of this article is to present an efficient extension of Rosenthal's order-n algorithm to multibody systems containing closed loops. The equations of motion are created by using relative coordinates and partial velocity 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 equation of motion as a differential-algebraic equation (DAE) rather than an ordinary differential equation. This DAE is then solved by applying the extended Rosenthal's order-n algorithm proposed in this article. While solving DAE, violation of the kinematic constraint equations of cut joints is corrected by coordinate projection method. Some numerical simulations are carried out to demonstrate efficiency of the proposed method.