Now we will switch to the formulation of mechanics due to Lagrange. The advantages will be that it is much more general, and can incorporate systems that cannot be described in Newtonian mechanics. The method of Lagrange is very suitable for including symmetry, and is the basis for field theory where we work with continuous systems with infinite numbers of variables. Relativity is also easily included. Finally, in many cases not all variables are free, we often have constraints, and they can be included easily.
Constraints come in many forms.
Other constraints are in terms of inequalities. These are in general much harder to include. One way to include constraints is to reduce the number of free coordinates. We switch to so-called generalized coordinates . These variables are often labeled by q's and our generalized coordinates are .