ABSTRACT
This chapter considers the process of forward dynamics for unconstrained and then for constrained formulations. It examines several methods to control constraint violations due to numerical integration errors. The chapter discusses how to perform forward dynamic analysis on systems that involve impact, constraint addition during motion, or any form of discontinuities in velocities. It considers the joint-coordinate formulation of the equations of motion for the variable-length pendulum as a set of unconstrained differential equations. The chapter also considers the body-coordinate formulation of the equations of motion for the same system. It discusses several techniques for controlling the growth of the constraint violation or eliminating it completely. The chapter includes statements to recompute the constraint violations at every reported time step. It discusses how to perform kinematic and inverse dynamic analyses by integration as presented for forward dynamic analysis in Algorithm C.
