Constraint

Constraint

A restriction on the natural degrees of freedom of a system. If n and m are the numbers of the natural and actual degrees of freedom, the difference n - m is the number of constraints. In principle n = 3N, where N is the number of particles, for example, atoms. In practice n is determined by the number of effectively rigid components.

A holonomic system is one in which the n original coordinates can be expressed in terms of m independent coordinates and possibly also the time. It is characterized by frictionless contacts and inextensible linkages. The new coordinates are called generalized coordinates. See Lagrange's equations

Nonholonomic systems cannot be reduced to independent coordinates because the constraints are not on the n coordinate values themselves but on their possible changes. For example, an ice skate may point in all directions but at each position it must point along its path. See Degree of freedom (mechanics)

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(programming, mathematics)

constraint - A Boolean relation, often an equality or ineqality relation, between the values of one or more mathematical variables (often two). E.g. x>3 is a constraint on x. constraint satisfaction attempts to assign values to variables so that all constraints are true. Usenet newsgroup: news:comp.constraints. FAQ.