ABSTRACT
In Chapter 10, the basic problem of the calculus of variations was modified by imposing equality constraints on auxiliary integrals of functions of x, y, and y′, i.e., isoperimetric constraints. Other problems in the calculus of variations involve equality or inequality constraints on functions of x, y and y′ at all points in (a, b). When a pointwise equality constraint involves only the vector unknowns y = (y 1(x), y 2(x), …, yn (x)) T (and possibly also x explicitly), it is called a holonomic constraint, otherwise it is called a nonholonomic constraint. We have already encountered some problems with holonomic constraints in Chapter 7. We shall see in the next chapter that the isoperimetric constraints of Chapter 10 are, in fact, equivalent to a certain kind of nonholonomic constraints.
