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If the system is neither stable nor marginally stable, it is unstable. If the system is in state space representation, marginal stability can be analyzed by deriving the Jordan normal form: [2] if and only if the Jordan blocks corresponding to poles with zero real part are scalar is the system marginally stable.
The simplest kind of an orbit is a fixed point, or an equilibrium. If a mechanical system is in a stable equilibrium state then a small push will result in a localized motion, for example, small oscillations as in the case of a pendulum. In a system with damping, a stable equilibrium state is moreover asymptotically stable. On the other hand ...
The state is neutral to the lowest order and nearly remains in equilibrium if displaced a small amount. To investigate the precise stability of the system, higher order derivatives can be examined. The state is unstable if the lowest nonzero derivative is of odd order or has a negative value, stable if the lowest nonzero derivative is both of ...
In chemistry, chemical stability is the thermodynamic stability of a chemical system, in particular a chemical compound or a polymer. [1]Chemical stability may also refer to the shelf-life of a particular chemical compound; that is the duration of time before it begins to degrade in response to environmental factors.
More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis). The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge.
Depending on the size of the velocity difference and the size of the density contrast between the layers, Kelvin-Helmholtz waves can look different. For instance, between two layers of air or two layers of water, the density difference is much smaller and the layers are miscible; see black-and-white model video.
For a tailless aircraft, the neutral point coincides with the aerodynamic center, and so for such aircraft to have longitudinal static stability, the center of gravity must lie ahead of the aerodynamic center. [13] For missiles with symmetric airfoils, the neutral point and the center of pressure are coincident and the term neutral point is not ...
The relation between the two is E ea = −ΔE(attach). However, if the value assigned to E ea is negative, the negative sign implies a reversal of direction, and energy is required to attach an electron. In this case, the electron capture is an endothermic process and the relationship, E ea = −ΔE(attach) is still valid. Negative values ...