Indynamical systemsinstability means that some of the outputs or internalstates increase with time, without bounds.[1] Not all systems that are notstable are unstable; systems can also bemarginally stable or exhibitlimit cycle behavior.
Instructural engineering, a structural beam or column can become unstable when excessive compressive load is applied. Beyond a certain threshold, structuraldeflections magnifystresses, which in turn increases deflections. This can take the form ofbuckling or crippling. The general field of study is calledstructural stability.
Atmospheric instability is a major component of allweather systems on Earth.
In the theory ofdynamical systems, astate 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.
Incontinuous timecontrol theory, a system is unstable if any of theroots of itscharacteristic equation hasreal part greater than zero (or if zero is a repeated root). This is equivalent to any of theeigenvalues of thestate 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.[clarification needed] The equivalent condition indiscrete 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.
Fluid instabilities occur inliquids,gases andplasmas, and are often characterized by the shape that form; they are studied influid dynamics andmagnetohydrodynamics. Fluid instabilities include:
Plasma instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic instabilities. Plasma instabilities are also categorised into different modes – seethis paragraph in plasma stability.
Galaxies andstar clusters can be unstable, if small perturbations in thegravitational 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:
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.[6] Injuries causeproprioceptive 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 idealcenter 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 causedeafferentation, the interruption of sensory nerve fibers, and functional instability, then a subject's postural sway should be altered.[7] 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.