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:
“Two things in America are astonishing: the changeableness of most human behavior and the strange stability of certain principles. Men are constantly on the move, but the spirit of humanity seems almost unmoved.”
—Alexis de Tocqueville (1805–1859)
“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)
“I was not at all shocked with this execution at the time. John died seemingly without much pain. He was effectually hanged, the rope having fixed upon his neck very firmly, and he was allowed to hang near three quarters of an hour; so that any attempt to recover him would have been in vain. I comforted myself in thinking that by giving up the scheme I had avoided much anxiety and uneasiness.”
—James Boswell (1740–1795)
“A bath and a tenderloin steak. Those are the high points of a man’s life.”
—Curtis Siodmak (1902–1988)