In a physical system a particle may be constrained to move on the surface of a sphere, a bead on a wire, or gas molecules within a container.  Similarly we can recognize that entities in an organization may experience constraints upon their actions that are not just the relation force applied by other entities within the organization.

If the conditions of constraint can be expressed as equations connecting the coordinates of the particles (and the time) having the form

                                     (3.15)

then the constraints are said to be holonomic.

A bead on a wire and most ecological constraints are holonomic.  The gas in a container and a maximum information processing capacity of an entity are nonholonomic, because the equation relating the coordinates is an inequality and not of the form of equation (3.15).

Constraints introduce two types of difficulties in the solution of problems.  First, the coordinates are no longer all independent, since they are connected by the equations of constraint.  Second, the relation forces of constraint, e.g., the relation force on the entity experiencing the constraint are not known.  They are among the unknowns of the problem and must be obtained from the solution we seek.

In the case of holonomic constraints, the first difficulty is solved by introducing generalized coordinates.  We have been considering a system of N entities with N(N-1)/2 independent degrees of freedom.  If there exist holonomic constraints, expressed in k equations in the form of 8.15, then we have (N(N-1)/2)-k degrees of freedom or independent coordinates.  This can be expressed with a new set of coordinates via transformation equations.

…                                                                                 (3.16)

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