Instability
In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be 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 deflections magnify 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 systems on Earth.
Instability in control systems
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 roots of its characteristic equation has real part greater than zero. This is equivalent to any of the eigenvalues of the 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. 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
- Baroclinic instability
Fluid instabilities
- Ballooning instability ; found in the magnetosphere
- Atmospheric instability
- * Hydrodynamic instability or dynamic instability
- ** Inertial instability; baroclinic instability; symmetric instability, conditional symmetric or convective symmetric instability; barotropic instability; Helmholtz or shearing instability; rotational instability
- * Hydrostatic instability or static instability/vertical instability, thermodynamic instability
- ** Conditional or static instability, buoyant instability, latent instability, nonlocal static instability, conditional-symmetric instability; convective, potential, or thermal instability, convective instability of the first and second kind; absolute or mechanical instability
- Bénard instability
- Drift mirror instability
- Kelvin–Helmholtz instability
- Rayleigh–Taylor instability
- Saffman–Taylor instability
- Plateau-Rayleigh instability
- Richtmyer-Meshkov instability
- Shock Wave Instability
- Benjamin-Feir Instability
Plasma instabilities
Instabilities of stellar systems
and star clusters 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" or rounder than before. Instabilities in stellar systems include:- Bar instability of rapidly rotating disks
- Jeans instability
- Firehose instability
- Gravothermal instability
- Radial-orbit instability
- Various instabilities in cold rotating disks
Joint instabilities