method on systems of more than three variables to use common sense as to whether the system in question is holonomic, and only pursue testing if the system likely is not. Additionally, it is likewise best to use mathematical intuition to try to predict which test would fail first and begin with that one, skipping tests at first that seem likely to succeed. If every test equation is true for the entire set of combinations for all constraint equations, the system is holonomic. If it is untrue for even one test combination, the system is nonholonomic. Example Consider this dynamical system described by a constraint equation in Pfaffian form. The configuration space, by inspection, is . Because there are only three terms in the configuration space, there will be only one test equation needed. We can organize the terms of the constraint equation as such, in preparation for substitution: Substituting the terms, our test equation becomes: After calculating all partial derivatives, we get: Simplifying, we find that: We see that our test equation is true, and thus, the system must be holonomic. We have finished our test, but now knowing that the system is holonomic, we may wish to find the holonomic constraint equation. We can attempt to find it by integrating each term of the Pfaffian form and attempting to unify them into one equation, as such: It's easy to see that we can combine the results of our integrations to find the holonomic constraint equation: where C is the constant of integration. Constraints of constant coefficients For a given Pfaffian constraint where every coefficient of every differential is a constant, in other words, a constraint in the form: the constraint must be holonomic. We may prove this as follows: consider a system of constraints in Pfaffian form where every coefficient of every differential is a constant, as described directly above. To test whether this system of constraints is holonomic, we use the universal test. We can see that in the test equation, there are three terms that must sum to zero. Therefore, if each of those three terms in every possible test equation are each zero, then all test equations are true and this the system is holonomic. Each term of each test equation is in the form: where: , , and are some combination (with total combinations) of and for a given constraint . , , and