Editing Instability

{{short description|Characterized by some of the outputs or internal states growing without bounds}}
{{About||inherently unstable aircraft|Relaxed stability|the political science concept|Failed state}}
{{redirect|Unstable}}

[[File:Unstable3.svg|thumb|A ball on the top of a hill is an unstable situation.]]
In [[dynamical system]]s '''instability''' means that some of the outputs or internal [[state (controls)|states]] increase with time, without bounds.<ref>{{cite web|url=http://www.merriam-webster.com/dictionary/instability|title=Definition of INSTABILITY|website=www.merriam-webster.com|access-date=23 April 2018}}</ref>  Not all systems that are not [[Stability theory|stable]] are unstable; systems can also be [[marginal stability|marginally stable]] or exhibit [[limit cycle]] behavior.

In [[structural engineering]], a structural beam or column can become unstable when excessive compressive load is applied. Beyond a certain threshold, structural [[Deflection (engineering)|deflection]]s magnify [[stress (physics)|stresses]], which in turn increases deflections. This can take the form of [[buckling]] or crippling. The general field of study is called [[structural stability]].

[[Atmospheric instability]] is a major component of all [[weather system]]s on Earth.

==Instability in control systems==
{{See also|Stabilizability}}

In the theory of [[dynamical systems]], a [[state variable]] in a system is said to be unstable if it evolves without bounds. A system itself is said to be unstable if at least one of its state variables is unstable.

In [[continuous time]] [[control theory]], a system is unstable if any of the [[Root of a function|roots]] of its [[Characteristic equation (calculus)|characteristic equation]] has [[real part]] greater than zero (or if zero is a repeated root).  This is equivalent to any of the [[eigenvalues]] of the [[State space (controls)|state matrix]] having either real part greater than zero, or, for the eigenvalues on the imaginary axis, the algebraic multiplicity being larger than the geometric multiplicity.{{clarify|reason=what is the difference between these two types of multiplicity?|date=September 2015}} The equivalent condition in [[discrete time]] is that at least one of the eigenvalues is greater than 1 in absolute value, or that two or more eigenvalues are equal and of unit absolute value.

==Instability in solid mechanics==
* [[Buckling]]
* [[Elastic instability]]
* [[Drucker stability]] of a nonlinear constitutive model
* Biot instability (surface wrinkling in elastomers)
* Baroclinic instability <ref>{{cite web|url=http://www.merriam-webster.com/dictionary/baroclinic+instability|title=Definition of BAROCLINIC INSTABILITY|website=www.merriam-webster.com|access-date=23 April 2018}}</ref>

==Fluid instabilities==
[[File:HD-Rayleigh-Taylor.gif|thumb|[[Hydrodynamic]]s simulation of the [[Rayleigh–Taylor instability]]<ref>{{cite web |author=Shengtai Li |author2=Hui Li |title=Parallel AMR Code for Compressible MHD or HD Equations |publisher=Los Alamos National Laboratory |url=http://math.lanl.gov/Research/Highlights/amrmhd.shtml |access-date=2006-05-31 |archive-url=https://web.archive.org/web/20160303182548/http://math.lanl.gov/Research/Highlights/amrmhd.shtml |archive-date=2016-03-03  }}</ref> ]]
[[File:Fluid Instability.jpg|thumb|Unstable flow structure generated from the collision of two impinging jets.]]

[[Fluid]] instabilities occur in [[liquids]], [[gases]] and [[Plasma physics|plasmas]], and are often characterized by the shape that form; they are studied in [[fluid dynamics]] and [[magnetohydrodynamics]]. Fluid instabilities include:

* [[Ballooning instability]] (some analogy to the Rayleigh–Taylor instability); found in the [[magnetosphere]]
* [[Atmospheric instability]]
** [[Hydrodynamic instability]] or [[dynamic instability]] ([[atmospheric dynamics]])
*** [[Inertial instability]]; [[baroclinic instability]]; [[symmetric instability]], [[conditional symmetric instability|conditional symmetric]] or [[conditional symmetric instability|convective symmetric instability]]; [[barotropic instability]]; [[Helmholtz instability|Helmholtz]] or [[Helmholtz instability|shearing instability]]; [[rotational instability]]
** [[Hydrostatic instability]] or [[static instability]]/[[static instability|vertical instability]] ([[static instability|parcel instability]]), [[thermodynamic instability]] ([[atmospheric thermodynamics]])
*** [[Conditional instability|Conditional]] or [[static instability]], [[buoyant instability]], [[latent instability]], [[nonlocal static instability]], [[conditional-symmetric instability]]; [[convective instability|convective]], [[convective instability|potential]], or [[convective instability|thermal instability]], [[convective instability of the first kind|convective instability of the first]] and [[convective instability of the second kind|second kind]]; [[absolute instability|absolute]] or [[absolute instability|mechanical instability]]
* [[Bénard cells|Bénard instability]]
* Drift mirror instability
* [[Kelvin–Helmholtz instability]] (similar, but different from the [[diocotron instability]] in plasmas)
* [[Rayleigh–Taylor instability]]
* [[Saffman–Taylor instability]]
* [[Plateau-Rayleigh instability]] (similar to the Rayleigh–Taylor instability)
* [[Richtmyer-Meshkov instability]] (similar to the Rayleigh–Taylor instability)
* [[shock wave|Shock Wave]] Instability
* [[Modulational instability|Benjamin-Feir Instability]] (also known as modulational instability)

==Plasma instabilities==
{{Main|Plasma stability#Plasma instabilities}}
[[Plasma (physics)|Plasma]] instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic instabilities. Plasma instabilities are also categorised into different modes&nbsp;– see [[Plasma stability#Plasma instabilities|this paragraph in plasma stability]].

==Instabilities of stellar systems==

[[Galaxies]] and [[star cluster]]s can be unstable, if small perturbations in the [[gravitational potential]] cause changes in the density that reinforce the original perturbation.  Such instabilities usually require that the motions of stars be highly correlated, so that the perturbation is not "smeared out" by random motions. After the instability has run its course, the system is typically "hotter" (the motions are more random) or rounder than before. Instabilities in stellar systems include:

* [[Bar instability]] of rapidly rotating disks
* [[Jeans instability]]
* [[Firehose instability]]<ref name="MS94">{{citation
 | last1 = Merritt | first1 = D.
 | author1-link = David Merritt
 | last2 = Sellwood | first2 = J.
 | title=Bending Instabilities of Stellar Systems
 | journal=The Astrophysical Journal
 | volume=425
 | year=1994
 | pages=551–567
 | doi=10.1086/174005
 | bibcode=1994ApJ...425..551M
}}</ref>
* [[Gravothermal instability]]<ref>{{citation
 | title=The Gravothermal Instability at All Scales: From Turnaround Radius to Supernovae
 | last=Roupas | first=Zacharias
 | journal=Universe | volume=5 | issue=1 | page=12
 | date=January 2019 | doi=10.3390/universe5010012
 | arxiv=1809.07568 | bibcode=2019Univ....5...12R 
| doi-access=free }}</ref>
* [[Radial-orbit instability]]
* Various instabilities{{which|date=December 2019}} in cold rotating disks

==Joint instabilities==
The most common residual disability after any sprain in the body is instability.  Mechanical instability includes insufficient stabilizing structures and mobility that exceed the physiological limits.  Functional instability involves recurrent sprains or a feeling of giving way of the injured joint.<ref>{{cite journal |last1=Guskiewicz |first1=K. M. |first2=David H. |last2=Perrin |title=Effect of Orthotics on Postural Sway Following Inversion Ankle Sprain |journal=Journal of Orthopedic and Sports Physical Therapy |volume=23 |issue=5 |pages=326–331  |date=1996 |doi=10.2519/jospt.1996.23.5.326 |pmid=8728531 |doi-access=free }}<!--|access-date=15 October 2013--></ref>  Injuries cause [[proprioceptive]] deficits and impaired postural control in the joint.  Individuals with muscular weakness, occult instability, and decreased postural control are more susceptible to injury than those with better postural control.  Instability leads to an increase in postural sway, the measurement of the time and distance a subject spends away from an ideal [[Center of pressure (terrestrial locomotion)|center of pressure]].  The measurement of a subject's postural sway can be calculated through testing center of pressure (CoP), which is defined as the vertical projection of center of mass on the ground.  Investigators have theorized that if injuries to joints cause [[deafferentation]], the interruption of sensory nerve fibers, and functional instability, then a subject's postural sway should be altered.<ref>{{cite journal |first1=A. |last1=Pintsaar |last2=Brynhildsen |first2=J. |first3=H. |last3=Tropp |title=Postural Corrections after Standardised Perturbations of Single Limb Stance: Effect of Training and Orthotic Devices in Patients with Ankle Instability |journal=[[British Journal of Sports Medicine]] |volume=30 |issue=2 |pages=151–155 |date=1996 |doi=10.1136/bjsm.30.2.151 |pmid=8799602 |pmc=1332381 }}<!--|access-date=15 October 2013--></ref> Joint stability can be enhanced by the use of an external support system, like a brace, to alter body mechanics.  The mechanical support provided by a brace provides cutaneous afferent feedback in maintaining postural control and increasing stability.

==Notes==
{{Reflist}}

==External links==
* [http://www.efluids.com/efluids/pages/gallery.htm eFluids Fluid Flow Image Gallery]

[[Category:Systems theory]]
[[Category:Fluid mechanics]]
[[Category:Plasma phenomena]]
[[Category:Stability theory]]