13.2.1 Reducing Degree by Increasing Dimension

Taking into account constraints on higher order derivatives seems substantially more complicated. This section explains a convenient trick that converts constraints that have higher order derivatives into a new set of constraints that has only first-order derivatives. This involves the introduction of a phase space, which has more dimensions than the original C-space. Thus, there is a trade-off because the dimension is increased; however, it is widely accepted that increasing the dimension of the space is often easier than dealing with higher order derivatives. In general, the term state space will refer to either C-spaces or phase spaces derived from them.