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About: Poisson bracket
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The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables (below symbolized by and , respectively) that satisfy canonical Poisson bracket relations. The set of possible canonical transformations is always very rich. 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to /sparql endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div> <!-- /navbar --> <!-- page-header --> <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/Poisson_bracket">Poisson bracket</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/ontology/MilitaryConflict">military conflict</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables (below symbolized by and , respectively) that satisfy canonical Poisson bracket relations. The set of possible canonical transformations is always very rich. For instance, it is often possible to choose the Hamiltonian itself as one of the new canonical momentum coordinates</p> </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Simeon_Poisson.jpg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ar" >في الرياضيات والميكانيكا الكلاسيكية قوس بواسون هو عملية ثنائية مهمة في الميكانيكا الهاملتونية، حيث يلعب دورًا مركزيًا في معادلات هاملتون للحركة التي تؤثر في تحول الوقت في نظام هاملتون الديناميكي، كما يميز قوس بواسون فئة معينة من التحولات الإحداثية تسمى التحولات الكنسية، والتي بدورها تحول الأنظمة الإحداثية الكنسية إلى أنظمة إحداثية أساسية، حيث يتكون «النظام الإحداثي الكنسي» من متغيران هما: الموقع الكنسي والزخم، ويرمز إليهما أدناه ب: و على التوالي حيث يخضعان لعلاقات قوس بواسون الكنسي، كما أن هناك دائمًا مجموعة من التحولات الكنسية المحتملة ذات قيمة عالية، على سبيل المثال غالبًا ما يكون من الممكن اختيار دالة هاملتونيان نفسها كأحد إحداثيات الزخم الكنسي الجديدة. بمعنى أكثر عمومية يُستخدم قوس بواسون لتحديد جَبْر بواسون،حيث يُعتبر جبر الاقترانات على متشعب بواسون حالة خاصة، وهناك أمثلةٌ عامةٌ أخرى كالذي يحدث في نظرية جبر لاي لتشكيل جبر بواسون من جبر الموتر لجبر لاي،حيث أُعطيَ بناءٌ مُفصّل لكيفية حدوث ذلك في مقالة الجبر الشامل المغلف الإنجليزية، والتشوهات الكمومية للجبر الشامل المغلف تؤدي إلى تدوين مجموعات الكم. كل هذه المواضيع سُميت تكريمًا لسيمون دينيس بواسون.</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="cs" >Poissonova závorka označuje matematický výraz používaný v matematice a klasické mechanice (konkrétně v Hamiltonovské mechanice), kde se využívá k popisu časového vývoje dynamického systému. V matematice se Poissonova závorka používá k definici (příkladem Poissonovy algebry je ). Poissonova závorka je pojmenována po Siméonu-Denisi Poissonovi.</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="de" >Die Poisson-Klammer, benannt nach Siméon Denis Poisson, ist ein bilinearer Differentialoperator in der kanonischen (hamiltonschen) Mechanik. Sie ist ein Beispiel für eine Lie-Klammer, also für eine Multiplikation in einer Lie-Algebra.</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="es" >En matemáticas y mecánica clásica, el corchete de Poisson es un importante operador de la mecánica hamiltoniana, actuando como pieza fundamental en la definición de la evolución temporal de un sistema dinámico en la formulación hamiltoniana. Desde un punto de vista más general, el corchete de Poisson se usa para definir un álgebra de Poisson, de las que las variedades de Poisson son un caso especial. Todas estas están nombradas en honor a Siméon Denis Poisson.</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >En mécanique hamiltonienne, on définit le crochet de Poisson de deux observables et , c'est-à-dire de deux fonctions sur l'espace des phases d'un système physique, par : où les variables, dites canoniques, sont les coordonnées généralisées et les moments conjugués . C'est un cas particulier de crochet de Lie. Avant de continuer, soulignons au passage qu'il existe deux conventions de signes au crochet de Poisson.La définition donnée ci-haut est dans la convention de signe employée par Dirac, Arnold , Goldstein et de Gosson pour n'en citer que quelques-uns.La convention de signe opposée est celle adoptée par Landau et Lifschitz , Souriau , Kirillov , Woodhouse puis McDuff et Salamon : Plus bas, on dira plus simplement que la première convention de signe du crochet de Poisson est celle de Dirac et que la seconde convention de signe est celle de Landau et Lifschitz. Notons que cette nomenclature n'est pas standard et ne vise qu'à enlever l'ambiguïté sur le signe du crochet de Poisson. Quelle convention de signe fut celle de Lagrange ou d'Hamilton par exemple ?</span><small> (fr)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables (below symbolized by and , respectively) that satisfy canonical Poisson bracket relations. The set of possible canonical transformations is always very rich. For instance, it is often possible to choose the Hamiltonian itself as one of the new canonical momentum coordinates. In a more general sense, the Poisson bracket is used to define a Poisson algebra, of which the algebra of functions on a Poisson manifold is a special case. There are other general examples, as well: it occurs in the theory of Lie algebras, where the tensor algebra of a Lie algebra forms a Poisson algebra; a detailed construction of how this comes about is given in the universal enveloping algebra article. Quantum deformations of the universal enveloping algebra lead to the notion of quantum groups. All of these objects are named in honor of Siméon Denis Poisson.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="it" >In matematica e meccanica classica, una parentesi di Poisson, introdotta nel 1809 da Siméon-Denis Poisson, è un'operazione binaria che riveste un ruolo di primo piano nella meccanica hamiltoniana, essendo sfruttata nelle equazioni di Hamilton del moto che descrivono l'evoluzione temporale di un sistema dinamico hamiltoniano. Si tratta di un caso particolare della parentesi di Jacobi. In generale la parentesi di Poisson viene utilizzata per definire un', di cui l'algebra delle funzioni definite su una varietà di Poisson sono un caso speciale. Si tratta di una costruzione differenziale della forma: dove e sono funzioni di variabili e . In termini più rigorosi, e generali, le parentesi di Poisson rappresentano in forma compatta il prodotto scalare simplettico tra i gradienti di due funzioni.</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ja" >ポアソン括弧(ぽあそんかっこ、英: Poisson Bracket)とは、ハミルトン形式の解析力学における重要概念の一つ。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="nl" >In het hamiltonformalisme wordt de poisson-haak voor twee dynamische grootheden en als volgt gedefinieerd: waarbij de coördinaten in de faseruimte zijn. Dit begrip werd door de Franse wiskundige Siméon Poisson in 1809 ingevoerd. De poisson-haak in de klassieke mechanica komt overeen met de commutator in de kwantummechanica.</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ko" >푸아송 괄호(영어: Poisson bracket)란 해밀턴 역학에서 쓰이는 중요한 연산자로, 어떤 물리량의 시간적 변화를 기술하는 데 중요한 역할을 하고 있다. 좀 더 일반적인 방법으로, 푸아송 괄호는 푸아송 다양체의 를 정의하는 데 쓰인다. 위의 푸아송과 관련된 이름을 가진 것들은 모두 프랑스의 물리학자이자 수학자인 푸아송의 이름에서 따온 이름들이다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pl" >Nawias Poissona – pojęcie z dziedziny fizyki matematycznej, głównie mechaniki klasycznej, a konkretniej mechaniki Hamiltona. Występuje m.in. w kanonicznych równaniach Hamiltona, które opisują ewolucję w czasie układu fizycznego. Nawias Poissona to działanie dwuargumentowe na zbiorze wielkości fizycznych. Nawiasy Poissona służą też do definicji algebry Poissona (por. dalej). Są tak nazwane na cześć francuskiego matematyka Siméona Denisa Poissona.</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pt" >O Parênteses de Poisson(ou os colchetes de Poisson) de duas funções u e v das variáveis canônicas qi e pi é definido como: .</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="uk" >Дужками Пуассона в класичній механіці називається вираз де й — будь-які функціїузагальнених координат та узагальнених імпульсів, — кількість ступенів свободи системи. Пуассонова дужка є класичним аналогом квантового комутатора.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ru" >Ско́бки Пуассо́на (также возможно ско́бка Пуассо́на и скобки Ли) — оператор, играющий центральную роль в определении эволюции во времени динамической системы. Эта операция названа в честь С.-Д. Пуассона.Рассматривался С. Пуассоном в 1809 году, затем забыт и переоткрыт Карлом Якоби.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="zh" >在數學及经典力學中，泊松括號是哈密顿力學中重要的運算，在哈密頓表述的動力系統中時間演化的定義起着中心角色。在更一般的情形，泊松括号用来定义一个泊松代数，而泊松流形是一个特例。它们都是以西莫恩·德尼·泊松命名的。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail"><small>dbo:</small>thumbnail</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Simeon_Poisson.jpg?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/Simeon_Poisson.jpg?width=300"><small>wiki-commons</small>:Special:FilePath/Simeon_Poisson.jpg?width=300</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" 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href="http://dbpedia.org/class/yago/Statement106722453"><small>yago</small>:Statement106722453</a></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment"><small>rdfs:</small>comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="cs" >Poissonova závorka označuje matematický výraz používaný v matematice a klasické mechanice (konkrétně v Hamiltonovské mechanice), kde se využívá k popisu časového vývoje dynamického systému. V matematice se Poissonova závorka používá k definici (příkladem Poissonovy algebry je ). Poissonova závorka je pojmenována po Siméonu-Denisi Poissonovi.</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="de" >Die Poisson-Klammer, benannt nach Siméon Denis Poisson, ist ein bilinearer Differentialoperator in der kanonischen (hamiltonschen) Mechanik. Sie ist ein Beispiel für eine Lie-Klammer, also für eine Multiplikation in einer Lie-Algebra.</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="es" >En matemáticas y mecánica clásica, el corchete de Poisson es un importante operador de la mecánica hamiltoniana, actuando como pieza fundamental en la definición de la evolución temporal de un sistema dinámico en la formulación hamiltoniana. Desde un punto de vista más general, el corchete de Poisson se usa para definir un álgebra de Poisson, de las que las variedades de Poisson son un caso especial. Todas estas están nombradas en honor a Siméon Denis Poisson.</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ja" >ポアソン括弧(ぽあそんかっこ、英: Poisson Bracket)とは、ハミルトン形式の解析力学における重要概念の一つ。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="nl" >In het hamiltonformalisme wordt de poisson-haak voor twee dynamische grootheden en als volgt gedefinieerd: waarbij de coördinaten in de faseruimte zijn. Dit begrip werd door de Franse wiskundige Siméon Poisson in 1809 ingevoerd. De poisson-haak in de klassieke mechanica komt overeen met de commutator in de kwantummechanica.</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ko" >푸아송 괄호(영어: Poisson bracket)란 해밀턴 역학에서 쓰이는 중요한 연산자로, 어떤 물리량의 시간적 변화를 기술하는 데 중요한 역할을 하고 있다. 좀 더 일반적인 방법으로, 푸아송 괄호는 푸아송 다양체의 를 정의하는 데 쓰인다. 위의 푸아송과 관련된 이름을 가진 것들은 모두 프랑스의 물리학자이자 수학자인 푸아송의 이름에서 따온 이름들이다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pl" >Nawias Poissona – pojęcie z dziedziny fizyki matematycznej, głównie mechaniki klasycznej, a konkretniej mechaniki Hamiltona. Występuje m.in. w kanonicznych równaniach Hamiltona, które opisują ewolucję w czasie układu fizycznego. Nawias Poissona to działanie dwuargumentowe na zbiorze wielkości fizycznych. Nawiasy Poissona służą też do definicji algebry Poissona (por. dalej). Są tak nazwane na cześć francuskiego matematyka Siméona Denisa Poissona.</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pt" >O Parênteses de Poisson(ou os colchetes de Poisson) de duas funções u e v das variáveis canônicas qi e pi é definido como: .</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="uk" >Дужками Пуассона в класичній механіці називається вираз де й — будь-які функціїузагальнених координат та узагальнених імпульсів, — кількість ступенів свободи системи. Пуассонова дужка є класичним аналогом квантового комутатора.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ru" >Ско́бки Пуассо́на (также возможно ско́бка Пуассо́на и скобки Ли) — оператор, играющий центральную роль в определении эволюции во времени динамической системы. Эта операция названа в честь С.-Д. Пуассона.Рассматривался С. Пуассоном в 1809 году, затем забыт и переоткрыт Карлом Якоби.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="zh" >在數學及经典力學中，泊松括號是哈密顿力學中重要的運算，在哈密頓表述的動力系統中時間演化的定義起着中心角色。在更一般的情形，泊松括号用来定义一个泊松代数，而泊松流形是一个特例。它们都是以西莫恩·德尼·泊松命名的。</span><small> (zh)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ar" >في الرياضيات والميكانيكا الكلاسيكية قوس بواسون هو عملية ثنائية مهمة في الميكانيكا الهاملتونية، حيث يلعب دورًا مركزيًا في معادلات هاملتون للحركة التي تؤثر في تحول الوقت في نظام هاملتون الديناميكي، كما يميز قوس بواسون فئة معينة من التحولات الإحداثية تسمى التحولات الكنسية، والتي بدورها تحول الأنظمة الإحداثية الكنسية إلى أنظمة إحداثية أساسية، حيث يتكون «النظام الإحداثي الكنسي» من متغيران هما: الموقع الكنسي والزخم، ويرمز إليهما أدناه ب: و على التوالي حيث يخضعان لعلاقات قوس بواسون الكنسي، كما أن هناك دائمًا مجموعة من التحولات الكنسية المحتملة ذات قيمة عالية، على سبيل المثال غالبًا ما يكون من الممكن اختيار دالة هاملتونيان نفسها كأحد إحداثيات الزخم الكنسي الجديدة.</span><small> (ar)</small></span></li> <li><span class="literal"><span property="rdfs:comment" lang="en" >In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables (below symbolized by and , respectively) that satisfy canonical Poisson bracket relations. The set of possible canonical transformations is always very rich. For instance, it is often possible to choose the Hamiltonian itself as one of the new canonical momentum coordinates</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >En mécanique hamiltonienne, on définit le crochet de Poisson de deux observables et , c'est-à-dire de deux fonctions sur l'espace des phases d'un système physique, par : où les variables, dites canoniques, sont les coordonnées généralisées et les moments conjugués . C'est un cas particulier de crochet de Lie.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="it" >In matematica e meccanica classica, una parentesi di Poisson, introdotta nel 1809 da Siméon-Denis Poisson, è un'operazione binaria che riveste un ruolo di primo piano nella meccanica hamiltoniana, essendo sfruttata nelle equazioni di Hamilton del moto che descrivono l'evoluzione temporale di un sistema dinamico hamiltoniano. Si tratta di un caso particolare della parentesi di Jacobi. In generale la parentesi di Poisson viene utilizzata per definire un', di cui l'algebra delle funzioni definite su una varietà di Poisson sono un caso speciale.</span><small> (it)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ar" >قوس بواسون</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="cs" >Poissonova závorka</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="de" >Poisson-Klammer</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="es" >Corchete de Poisson</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >Crochet de Poisson</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="it" >Parentesi di Poisson</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ko" >푸아송 괄호</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ja" >ポアソン括弧</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="nl" >Poisson-haak</span><small> (nl)</small></span></li> <li><span class="literal"><span property="rdfs:label" lang="en" >Poisson bracket</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pl" >Nawias Poissona</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pt" >Parênteses de Poisson</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ru" >Скобка Пуассона</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="uk" >Дужки Пуассона</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="zh" >泊松括號</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.01r00_" href="http://rdf.freebase.com/ns/m.01r00_"><small>freebase</small>:Poisson bracket</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" 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