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# perturbation

/perr'teuhr bay"sheuhn/, n.
1. the act of perturbing.
2. the state of being perturbed.
3. mental disquiet, disturbance, or agitation.
4. a cause of mental disquiet, disturbance, or agitation.
5. Astron. deviation of a celestial body from a regular orbit about its primary, caused by the presence of one or more other bodies that act upon the celestial body.
[1325-75; < L perturbation- (s. of perturbatio; see PERTURB, -ATION); r. ME perturbacioun < AF < L, as above]

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in astronomy, deviation in the motion of a celestial object caused either by the gravitational force of a passing object or by a collision with it. For example, predicting the Earth's orbit around the Sun would be rather straightforward were it not for the slight perturbations in its orbital motion caused by the gravitational influence of the other planets. The search for an eighth planet, which culminated in the discovery of Neptune, was undertaken in part because some astronomers believed that the orbit of Uranus was being gravitationally perturbed by some object beyond it.

in mathematics, method for solving a problem by comparing it with a similar one for which the solution is known. Usually the solution found in this way is only approximate.

Perturbation is used to find the roots of an algebraic equation that differs slightly from one for which the roots are known. Other examples occur in differential equations. In a physical situation, an unknown quantity is required to satisfy a given differential equation and certain auxiliary conditions that define the values of the unknown quantity at specified times or positions. If the equation or auxiliary conditions are varied slightly, the solution to the problem will also vary slightly.

The process of iteration is one way in which a solution of a perturbed equation can be obtained. Let D represent an operation, such as differentiation, performed on a function, and let D + εP represent a new operation differing slightly from the first, in which ε represents a small constant. Then, if f is a solution of the common type of problem Df = cf, in which c is a constant, the perturbed problem is that of determining a function g such that (D + εP)g = cg. This last equation can also be written as (D - c)g = -εPg. Then the function g1 that satisfies the equation (D - c)g1 = -εPf is called a first approximation to g. The function g2 that satisfies the equation (D - c)g2 = -εPg1 is called a second approximation to g, and so on, with the nth approximation gn satisfying (D - c)gn = -εPgn-1. If the sequence g1, g2, g3, . . . , gn, . . . converges to a specific function, that function will be the required solution of the problem. The largest value of ε for which the sequence converges is called the radius of convergence of the solution.

Another perturbation method is to assume that there is a solution to the perturbed equation of the form f + εg1 + ε2g2 + . . . etc., in which the g1, g2, . . . etc., are unknown, and then to substitute this series into the equation, resulting in a collection of equations to solve corresponding to each power of ε.

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Universalium. 2010.

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• perturbation — [ pɛrtyrbasjɔ̃ ] n. f. • 1295 « trouble, angoisse »; lat. perturbatio 1 ♦ Irrégularité dans le fonctionnement d un système. ⇒ dérangement, dérèglement, déséquilibre, 2. trouble. La grève a provoqué des perturbations dans le métro. ♢ Astron.… …   Encyclopédie Universelle

• Perturbation — or perturb may refer to any of numerous concepts in several fields:* Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial… …   Wikipedia

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• "Perturbation" — (roman) Perturbation (Verstörung) est un roman de Thomas Bernhard paru en 1967. Avec cette œuvre Bernhard consolida sa notoriété en Autriche et en Allemagne et commença à être traduit à l étranger. Le roman est structuré en deux parties. Il se… …   Wikipédia en Français

• perturbation — Perturbation, Perturbatio, Comotio animi. Perturbation qui fait seicher une personne, Tabifica perturbatio. Perturbation d esprit, Morbus animi …   Thresor de la langue françoyse

• Perturbation — Per tur*ba tion, n. [L. perturbatio: cf. F. perturbation.] 1. The act of perturbing, or the state of being perturbed; esp., agitation of mind. [1913 Webster] 2. (Astron.) A disturbance in the regular elliptic or other motion of a heavenly body,… …   The Collaborative International Dictionary of English

• Perturbation — (v. lat.), 1) Trübung, Störung; 2) die Abweichung, welche ein Himmelskörper in seiner Bahn um einen anderen durch die Gravitation eines ihm nahen dritten Weltkörpers erleidet. Die Berechnung derselben, namentlich auf die große Zahl der Weltkörper …   Pierer's Universal-Lexikon

• Perturbation — (lat.), Verwirrung, in den Gang von etwas eingreifende Störung; in der Astronomie, s. Störungen …   Meyers Großes Konversations-Lexikon

• Perturbation — Perturbatiōn (lat.), Störung, Verwirrung, Gemütsunruhe; polit. Umwälzung; in der Astronomie die Abweichungen der Himmelskörper von der reinen elliptischen Bewegung, erzeugt durch Gravitation gegen in der Nähe befindliche Massen (große Planeten).… …   Kleines Konversations-Lexikon

• perturbation — index apprehension (fear), commotion, confusion (ambiguity), consternation, distress (anguish) …   Law dictionary

• perturbation — late 14c., from O.Fr. perturbacion (14c.), from L. perturbationem, noun of action from perturbare (see PERTURB (Cf. perturb)) …   Etymology dictionary