A study of the augmented Lagrangian method for open loop and closed loop constrained multibody dynamic systems

Abstract

The primary objective of this thesis is to study the augmented Lagrangian method for open and closed loop constrained multibody dynamic systems. Much research has been carried out for the performance of the augmented Lagrangian formulation for open loop systems. This research extends the use of this formulation into the area of systems that contain closed loops. To gain insight into the behavior of the augmented Lagrangian formulation for dynamic analysis of multibody systems, it is necessary to have a practical means of creating the system-specific constraint equations and constraint Jacobian products. Two computer codes in the C language are created to be used together to implement the formulation for multibody systems containing spherical and/or revolute joints. An open loop system consisting of n bars suspended vertically from a pivot is used to study (1) the effect of the number of degrees of freedom and the Schur complement on the convergence of the Lagrange multipliers and accelerations, and (2) the effect that constraint violations can have on the total energy of the system in the absence of outside perturbations. To investigate the performance of the augmented Lagrangian method for closed loop systems, a vehicle suspension system is modeled. The work in this thesis lays the goundwork for numerical study of closed loop systems.