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Rigidity Argument
Rigid or rigidity may refer to: Mathematics and physics *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 (chemistry), the tendency of a substance to retain/maintain their shape when subjected to outside force *(Modulus of) rigidity or shear modulus (material science), the tendency of a substance to retain/maintain their shape when subjected to outside force Medicine *Rigidity (neurology), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as k = \frac where, * F is the force on the body * \delta is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring) In the International System of Units, stiffness is typically measured in newtons per meter (N/m). In Imperial units, stiffness is typically measured in pounds (lbs) per inch. Generally speaking, deflections (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Rigidity
In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges. Definitions Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility. In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges. A structure is rigid if it cannot flex; that is, if there is no continuous motion of the structure that preserves the shape of its rigid components and the pattern of their connections at the hinges. There are two essentially different kinds of rigidity. Finite or macroscopic rigidity means that the structure will not flex, fold, or bend by a positive amount. Infinitesimal rigidity means that the st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigidity (electromagnetism)
In accelerator physics, rigidity is 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'' = ''pc''/''q'', where ''B'' is the magnetic field, ''ρ'' is the gyroradius of the particle due to this field, ''p'' is the particle momentum, ''c'' is the speed of light and ''q'' is its charge. It is frequently referred to as simply "''Bρ''". The unit of the rigidity ''R'' is volts(N·m/C), a convenient unit is GV (''10^9'' V). In this case, unit of ''B'' is T(N·s/C·m), ''ρ'' is in the unit rad/s, ''p'' is in the unit kg· m/s, ''c'' is in the unit m/s, ''q'' is in the unit C. 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 perpendic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigidity (mathematics)
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. __FORCETOC__ Examples Some examples include: #Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values. #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. #By the fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Body
In physics, a rigid body (also known as a rigid object) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electrons and nuclei) are often seen as rigid bodies (see classification of molecules as rigid rotors). Kinematics Linear and angular position The position of a rigid body is the position of all the particles of which it is composed. To simplify the description of this position, we exploit the property that the body is rigi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Transformation
In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a proper rigid transformation, or rototranslation. Any proper rigid transformation can be decomposed into a rotation followed by a translation, while any improper rigid transformation can be decomposed into an improper rotation followed by a translation, or into a sequence of reflections. Any object wil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigidity (chemistry)
Rigid or rigidity may refer to: Mathematics and physics *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 (chemistry), the tendency of a substance to retain/maintain their shape when subjected to outside force *(Modulus of) rigidity or shear modulus (material science), the tendency of a substance to retain/maintain their shape when subjected to outside force Medicine *Rigidity (neurology), an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackrel\ \frac = \frac = \frac where :\tau_ = F/A \, = shear stress :F is the force which acts :A is the area on which the force acts :\gamma_ = shear strain. In engineering :=\Delta x/l = \tan \theta , elsewhere := \theta :\Delta x is the transverse displacement :l is the initial length of the area. The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M1L−1T−2, replacing ''force'' by ''mass'' times ''acceleration''. Explanation The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: * Young's modulus ''E'' describes the mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigidity (neurology)
Spasticity () is a feature of altered skeletal muscle performance with a combination of paralysis, increased tendon reflex activity, and hypertonia. It is also colloquially referred to as an unusual "tightness", stiffness, or "pull" of muscles. Clinically, spasticity results from the loss of inhibition of motor neurons, causing excessive velocity-dependent muscle contraction. This ultimately leads to hyperreflexia, an exaggerated deep tendon reflex. Spasticity is often treated with the drug baclofen, which acts as an agonist at GABA receptors, which are inhibitory. Spastic cerebral palsy is the most common form of cerebral palsy, which is a group of permanent movement problems that do not get worse over time. GABA's inhibitory actions contribute to baclofen's efficacy as an anti-spasticity agent. Cause Spasticity mostly occurs in disorders of the central nervous system (CNS) affecting the upper motor neurons in the form of a lesion, such as spastic diplegia, or upper motor neu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigidity (psychology)
In psychology, rigidity or mental 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. History Rigidity is an ancient part of our human cognition. 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 Max Wertheimer, Wolfgang Köhler, and Kurt Koffka in Germany. 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 tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Rigidity
In macroeconomics, rigidities are real prices and wages that fail to adjust to the level indicated by equilibrium or if something holds one price or wage fixed to a relative value of another. Real rigidities can be distinguished from nominal rigidities, rigidities that do not adjust because prices can be sticky and fail to change value even as the underlying factors that determine prices fluctuate. Real rigidities, along with nominal, are a key part of new Keynesian economics. Economic models with real rigidities lead to nominal shocks (like changes in monetary policy) having a large impact on the economy. In the product market Real price rigidity can result from several factors. First, firms with market power can raise their mark-ups to offset declines in marginal cost and maintain a high price. Search costs can contribute to real rigidities through "thick market externalities". A thick market has many buyers and sellers, so search costs are lower. Thick markets can be expecte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nominal Rigidity
Nominal rigidity, also known as price-stickiness or wage-stickiness, is a situation in which a nominal price is resistant to change. Complete nominal rigidity occurs when a price is fixed in nominal terms for a relevant period of time. For example, the price of a particular good might be fixed at $10 per unit for a year. Partial nominal rigidity occurs when a price may vary in nominal terms, but not as much as it would if perfectly flexible. For example, in a regulated market there might be limits to how much a price can change in a given year. If one looks at the whole economy, some prices might be very flexible and others rigid. This will lead to the aggregate price level (which we can think of as an average of the individual prices) becoming "sluggish" or "sticky" in the sense that it does not respond to macroeconomic shocks as much as it would if all prices were flexible. The same idea can apply to nominal wages. The presence of nominal rigidity is an important part of mac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
