Coupled holonomic constraints

Third, the use of coupled holonomic constraints having more complex forms than bond-stretch constraints highlights the limitations of the methods, which are not obvious when only simple bond-stretch constraints are employed. 

The most general form of holonomic constraint is nonlinear in the particle positions. Even the simple bond-stretch constraint is nonlinear. Consequently, Eq. [39] is in general a system of / coupled nonlinear equations, to be solved for the / unknowns (7). This nonlinear system of equations must be contrasted with the linear system of equations Eqs. [10] and [11] (which is also in general part of the method of undetermined parameters) used in the analytical method to solve for the Lagrangian multipliers and their derivatives. A solution of Eq. [39] can be achieved in two steps ... 

---