Also found in: Dictionary, Thesaurus, Legal, Wikipedia.


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)

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.


any restraining social influence which leads an individual to conform to social NORMS or social expectations.

For DURKHEIM, the distinctive SOCIAL FACTS, or sociological phenomena, that sociologists study can be recognized, above all, as ‘those ways of acting… capable of exercising an external constraint over the individual’. Durkheim recognized that such socially constraining forces may also be internalized by individuals, but it was an essential feature of his conception of such constraints that they had an origin external to the individual. Thus Durkheim's use of the term is much wider than the notion of ‘constraint’ in which the individual who wishes to act one way is made to act in another. As Lukes (1973) points out, Durkheim's use of the term ‘constraint’ at times suffers from considerable ambiguity failing to distinguish clearly between:

  1. the authority of legal rules, customs, etc. as manifested by the sanctions brought to bear on violators of these;
  2. the necessity of following rules to carry out certain activities successfully (e.g. the rules of language);
  3. the ‘causal influence’ of ‘morphological factors’ such as the influence of established channels of communication or transportation on commerce or migration;
  4. psychological compulsions in a crowd or social movement;
  5. cultural determination and the influence of SOCIALIZATION.

However, Durkheim's overall intention is clear: to draw attention to the fact that distinctively social reality constrains, and is ‘external’ to the individual, in each and any of the above senses. See also COLLECTIVE CONSCIENCE, FREE WILL, DETERMINISM.

Collins Dictionary of Sociology, 3rd ed. © HarperCollins Publishers 2000
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



(or reaction of a connection). For connections formed by bodies of any type, constraints are the forces of reaction of these bodies acting on points of the mechanical system. In contradistinction to active forces, constraints have values not known in advance. They depend not only on the type of connection but also on the active forces acting on the system; if the system is in motion, they depend additionally on how the system is moving. They are determined by solving the corresponding problems in mechanics. The directions of constraints or reactions in some cases are determined by the type of connection. Thus, if a point in the system is forced to remain always on a given smooth (frictionless) surface as a result of applied connections, then the reaction R is directed along the normal n

Figure 1. Examples of connections applied to a body P: (a) smooth surface, (b) smooth support, (c) inelastic flexible thread

to this surface (Figure 1). Figure 2 shows a smooth cylindrical hinge (bearing), for which two components (Rx and Ry) of the reaction are unknown, and a smooth ball and socket joint for which all three components (Rx, Ry, and Rz) of the reaction are unknown. For a rough surface, the constraint has two components: a normal and a tangential component; the latter is called the frictional force.

Figure 2. Examples of reactions with unknown components: (a) two unknown components, (b) three unknown components

In the general case, in solving problems in dynamics a restricted mechanical system is considered a free system if certain forces are applied to its points, such that the conditions imposed on the system by the connections are always satisfied when the system is in motion; these forces are called constraints.




a restriction imposed on the position or motion of a mechanical system. Constraints are usually realized by bodies. Examples of constraints are a surface along which a body slides or rolls, a thread by which a weight is suspended, and joints connecting the links of mechanisms. If the positions of points of a mechanical system relative to a given reference system are determined by the points’ Cartesian coordinates xk, yk, zk (k = 1, 2,…,n, where n is the number of points in the system), then the restrictions imposed by the constraints can be expressed in the form of equalities or inequalities that give the relation between the time t, the coordinates xk, yk, zk, and the first derivatives of the coordinates with respect to time k, k, żk (that is, the velocities of the points of the system).

Constraints that impose restrictions only on the positions (coordinates) of the points of a system and are expressed by equations of the form

(1) f(…, xk, yk, zk,…,t) = 0

are called geometric constraints. If the constraints also impose restrictions on the velocities of the points of the system, they are called kinematic constraints, and their equations are of the form

(2) Φ(…, xk, yk, zk,…, ẋk, k, żk,…,t) = 0

When equation (2) can be integrated with respect to time, the corresponding kinematic constraint is said to be integrable and is equivalent to a geometric constraint. Geometric and integrable kinematic constraints have the common name of holonomic constraints (seeHOLONOMIC SYSTEMS). Kinematic nonintegrable constraints are called nonholonomic (seeNONHOLONOMIC SYSTEMS).

Constraints that do not change with time are referred to as stationary constraints; their equations do not explicitly contain t. On the other hand, constraints that change with time are called moving constraints. Finally, two-way constraints are constraints such that to each virtual displacement of points of the system there corresponds a displacement in precisely the opposite direction. The equations of such constraints are of the form of equations (1) and (2). One-way constraints are constraints that do not satisfy the condition for two-way constraints. An example is a flexible thread, which permits displacement along the thread in only one direction. Such constraints are expressed by inequalities of the form f(…, xk, yk, zk,…)≥0.

The methods of solving problems in mechanics depend to a substantial degree on the nature of the constraints on the system. The effect of the action of constraints can be taken into account by introducing corresponding forces, called constraint forces. To determine these forces (or to eliminate the forces), constraint equations of the form (1) or (2) must be added to the equations of equilibrium or motion of the system. Ideal constraints are constraints for which the sum of the elementary works of all the forces in any virtual displacement of the system is equal to zero. Examples are a frictionless surface or flexible thread. For mechanical systems with ideal constraints, it is possible to obtain immediately equations of equilibrium or of motion that do not contain constraint forces by using the virtual work principle, the d’Alembert-Lagrange principle, or the Lagrange equations.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.


Anything that restricts the transverse contraction which normally occurs in a solid under longitudinal tension.
A restriction on the natural degrees of freedom of a system; the number of constraints is the difference between the number of natural degrees of freedom and the number of actual degrees of freedom.
(science and technology)
A condition imposed on a system which limits the freedom of the system; may be physical or mathematical, necessary or incidental.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


(programming, mathematics)
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.
This article is provided by FOLDOC - Free Online Dictionary of Computing (
References in periodicals archive ?
Cyan altitudes depict constraints to build a VNAV profile.
Different constraints act as stimuli for our creativity.
We can utilize this physical law as a constraint and learn to detect the object without resorting to exhaustive labeling.
With little time left in its five-year tenure, the federal government has directed power distribution companies to remove all constraints by the end of March in order to do away with load-shedding in areas covered by low-loss feeders across the country.
Energy sent out from Delta Power Plant on the same day was 340.76MW with a high-frequency constraint of 100 Hertz.
The CRWR and monitoring cells would be headed by GM, Chief Engineer to execute the constraints removal by the DISCOs at the end of
On the directions of Federal Minister for Power Division all Distribution Companies have already established CRWR while the PEPCO has established special monitoring cell headed by GM / Chief Engineer to execute the constraints removal by the DISCOs at the end of March 2018 enabling to enforce zero load shedding on 0-10% losses feeders across the country.
The DISCOs are further directed to equip the constraint removal war rooms with CCTV cameras connected with centralised monitoring system via communication link of Power information Technology Company (PITC) for continued monitoring by the federal minister for power division himself.
On the special directions of the minister for power, PEPCO and all the DISCOs have assessed and taken technical surveys of their existing distribution network and have identified points of constraints at 132K, 66KV, 11KV distribution transformers.
Most of the early published papers on constraint programming can be dated back to the 1970s.
The "facilitating" factors stand behind the individual's choice of leisure constraint negotiation (Hubbard & Mannell, 2001).

Full browser ?