13.1.1 Implicit vs. Parametric Representations

There are two general ways to represent differential constraints: parametric and implicit. Many parallels can be drawn to the parametric and implicit ways of specifying functions in general. Parametric representations are generally easier to understand and are simpler to use in applications. Implicit representations are more general but are often more difficult to utilize. The intuitive difference is that implicit representations express velocities that are prohibited, whereas parametric representations directly express the velocities that are allowed. In this chapter, a parametric representation is obtained wherever possible; nevertheless, it is important to understand both.