What is "rigidity"

Rigidity \Ri*gid"i*ty\, n. [L. rigiditas: cf. F. rigidit['e]. See Rigid.]

1. The quality or state of being rigid; want of pliability; the quality of resisting change of form; the amount of resistance with which a body opposes change of form; -- opposed to flexibility, ductility, malleability, and softness.

2. Stiffness of appearance or manner; want of ease or elegance.
   --Sir H. Wotton.

3. Severity; rigor. [Obs. orR.]
   --Bp. Burnet.

   Syn: Stiffness; rigidness; inflexibility.

1620s, from Latin rigiditas "stiffness," from rigidus (see rigid).

n. 1 The quality or state of being rigid; want of pliability; the quality of resisting change of form; the amount of resistance with which a body opposes change of form. 2 stiffness of appearance or manner; want of ease or elegance. 3 In Economics: synonym for sticky (of prices/wages etc.). Describing the tendency of prices and money wages to adjust to changes in the economy with a certain delay.

1. n. the physical property of being stiff and resisting bending [syn: rigidness]

2. the quality of being rigid and rigorously severe [syn: inflexibility] [ant: flexibility]

In mathematics, a rigid collection C of mathematical objects (for instance sets or functions) is one in which every c ∈ C is uniquely determined by less information about c than one would expect.

The above statement does not define a mathematical property. Instead, it describes in what sense the adjective rigid is typically used in mathematics, by mathematicians.

Some examples include:

1. Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values.
2. Holomorphic functions are determined by the set of all derivatives at a single point. A smooth function from the real line to the complex plane is not, in general, determined by all its derivatives at a single point, but it is if we require additionally that it be possible to extend the function to one on a neighbourhood of the real line in the complex plane. The Schwarz lemma is an example of such a rigidity theorem.
3. By the fundamental theorem of algebra, polynomials in C are rigid in the sense that any polynomial is completely determined by its values on any infinite set, say N, or the unit disk. Note that by the previous example, a polynomial is also determined within the set of holomorphic functions by the finite set of its non-zero derivatives at any single point.
4. Linear maps L(X, Y) between vector spaces X, Y are rigid in the sense that any L ∈ L(X, Y) is completely determined by its values on any set of basis vectors of X.
5. Mostow's rigidity theorem, which states that the geometric structure of negatively curved manifolds is determined by their topological structure.
6. A well-ordered set is rigid in the sense that the only ( order-preserving) automorphism on it is the identity function. Consequently, an isomorphism between two given well-ordered sets will be unique.
7. Cauchy's theorem on geometry of convex polytopes states that a convex polytope is uniquely determined by the geometry of its faces and combinatorial adjacency rules.
8. Alexandrov's uniqueness theorem states that a convex polyhedron in three dimensions is uniquely determined by the metric space of geodesics on its surface.

Rigid or rigidity may refer to:

• Stiffness, the property of a solid body to resist deformation, which is sometimes referred to as rigidity
• Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges
• Rigidity (electromagnetism), the resistance of a charged particle to deflection by a magnetic field
• Rigidity (mathematics), a property of a collection of mathematical objects (for instance sets or functions)
• Rigid body, in physics, a simplification of the concept of an object to allow for modelling.
• Rigid transformation, in mathematics, a rigid transformation preserves distances between every pair of points

• Rigidity (neurology), an increase in muscle tone leading to a resistance to passive movement throughout the range of motion
• Rigidity (psychology), an obstacle to problem solving which arises from over-dependence on prior experiences

• Real rigidity and nominal rigidity, the resistance of prices and wages to marketchanges in macroeconomics
• Ridgid, a brand of tools

cs:Rigidní de:Rigidität ja:固縮 ru:Ригидность sr:Ригидност

In psychology, rigidity refers to an obstinate inability to yield or a refusal to appreciate another person's viewpoint or emotions characterized by a lack of empathy. It can also refer to the tendency to perseverate, which is the inability to change habits and the inability to modify concepts and attitudes once developed. A specific example of rigidity is functional fixedness, which is a difficulty conceiving new uses for familiar objects. Systematic research on rigidity can be found tracing back to Gestalt psychologists, going as far back as the late 19th to early 20th century. With more than 100 years of research on the matter there is some established and clear data. Nonetheless, there is still much controversy surrounding several of the fundamental aspects of rigidity. In the early stages of approaching the idea of rigidity, it is treated as "a unidimensional continuum ranging from rigid at one end to flexible at the other". This idea dates back to the 1800s and was later articulated by Charles Spearman who described it as mental inertia. Prior to 1960 many definitions for the term rigidity were afloat. One example includes Kurt Goldstein's, which he stated, "adherence to a present performance in an inadequate way", another being Milton Rokeach saying the definition was, "[the] inability to change one's set when the objective conditions demand it".

In accelerator physics, rigidity is a concept used to determine the effect of particular magnetic fields on the motion of the charged particles.

It is a measure of the momentum of the particle, and it refers to the fact that a higher momentum particle will have a higher resistance to deflection by a magnetic field. It is defined as R = Bρ = p/q, where B is the magnetic field, ρ is the gyroradius of the particle due to this field, p is the particle momentum, and q is its charge. It is frequently referred to as simply "Bρ".

It is important to note that the rigidity is defined by the action of a static magnetic field, whose direction is perpendicular to the velocity vector of the particle. This will cause a force perpendicular both to the velocity vector, and to the field, defining a plane through which the particle moves. The definition of the Lorentz force implies that the particle's motion will be circular in a uniform field, thus giving a constant radius of curvature.

If the particle momentum, p, is given in GeV/c, then the rigidity, in tesla-metres, is Bρ = 3.3356p/q.