What is a Discontinuity?

What is a Discontinuity? A discontinuity can be defined as an event affecting the evolution of a dynamic system.

A good example occurs in the modeling of a hydraulic jack. The movement of the piston is limited by the physical dimensions of the jack body. If the piston is moving within the jack body and reaches the limit of its travel, it must be brought to rest or bounce.

In such a case, we consider that the velocity and displacement of the piston will reach a discontinuity.

Figure 1: ideal displacement and velocity of a piston (no bounce effect)

Other physical examples of discontinuities are

• backlash Backlash

• frictional stick-slip Frictional stick-slip

• any form of dead band

• hysteresis Hysteresis

• a valve such as a check valve that has characteristics when open which are completely different to when closed

• linear interpolation of tabulated data