ABSTRACT
This chapter aims to discuss the reader with some of the basic ideas of the nonlinear theory, and to present a number of important examples. An important point that must be clearly understood is that, while the theorem guarantees that the type of the critical point for the nonlinear system will be the same as the type for the associated linear system, the actual appearance of the paths may be different. A nonlinear spring is called hard or soft according to whether the magnitude of the restoring force increases more rapidly or less rapidly than a linear function of the displacement. The direction of the frictional force changes; so the solution follows a different circular trajectory up to the point C. At that moment, the block is stationary relative to the conveyor belt, and it will be carried along until the spring is stretched enough that the force of the spring can overcome the force of the friction.
