ABSTRACT
This chapter looks from a numerical standpoint more carefully into the long-term effects nonlinearities have on solutions. It aims to gain an intuitive feel for the influence that nonlinearities can have on solutions to differential equations. The chapter deals with a few mechanical systems that are subject to constraints. The field is vast and because of its importance and the implication of the results so far obtained, it is growing rapidly. First, linear problems are easier to treat. More importantly, however, near equilibrium the linear problems mimic the general properties of the nonlinear problems. Two-dimensional systems are easier to treat and easier to visualize than higher dimensional systems. The mathematical study of dynamical systems has been motivated partly by a desire to understand the behavior of real systems, partly by curiosity, and partly by the needs of modern science and technology.
