Stability of Fixed Points
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, for an unstable equilibrium, such as a ball resting on a top of a hill, certain small pushes will result in a motion with a large amplitude that may or may not converge to the original state.
There are useful tests of stability for the case of a linear system. Stability of a nonlinear system can often be inferred from the stability of its linearization.
Read more about this topic: Stability Theory
Famous quotes containing the words stability of, stability, fixed and/or points:
“No one can doubt, that the convention for the distinction of property, and for the stability of possession, is of all circumstances the most necessary to the establishment of human society, and that after the agreement for the fixing and observing of this rule, there remains little or nothing to be done towards settling a perfect harmony and concord.”
—David Hume (1711–1776)
“Every quotation contributes something to the stability or enlargement of the language.”
—Samuel Johnson (1709–1784)
“It is the fixed that horrifies us, the fixed that assails us with the tremendous force of mindlessness. The fixed is a Mason jar, and we can’t beat it open. ...The fixed is a world without fire--dead flint, dead tinder, and nowhere a spark. It is motion without direction, force without power, the aimless procession of caterpillars round the rim of a vase, and I hate it because at any moment I myself might step to that charmed and glistening thread.”
—Annie Dillard (b. 1945)
“When our relatives are at home, we have to think of all their good points or it would be impossible to endure them. But when they are away, we console ourselves for their absence by dwelling on their vices.”
—George Bernard Shaw (1856–1950)