ORDER-N FORMULATION OF EQUATIONS OF MOTION WITH EFFICIENT CHOICES OF MOTION VARIABLES

摘要

Order-n formulations of equations of motion of multibody systems are known to be computationally more efficient than order-n~3 formulations for large values of n, the system degrees of freedom. This paper extends to the order-n formulation the use of a newly proposed choice of motion variables that reduce computer time with the order- n~3 formulation. Kinematical equations needed for the first forward pass for revolute joints, Hooke's joints, ball-and-socket joints, and slider joints are given. In one example of a multibody system having hinges with ball-and-socket joint, Hooke's joint, and revolute joint, the new O(n) formulation is nearly ten times faster in execution than one using simple choice of motion variables. Computational efficiency is also demonstrated with a flexible body version of the same system. In another system with only revolute joints, there is no computational advantage with the new variables in the order-n formulation.