| dbo:abstract |
الكمية الثابتة في رياضيات النظام الديناميكي دالة للمتغيرات التابعة التي تظل قيمتها ثابتة على طول كل مسار للنظام. (ar) In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables, the value of which remains constant along each trajectory of the system. Not all systems have conserved quantities, and conserved quantities are not unique, since one can always produce another such quantity by applying a suitable function, such as adding a constant, to a conserved quantity. Since many laws of physics express some kind of conservation, conserved quantities commonly exist in mathematical models of physical systems. For example, any classical mechanics model will have mechanical energy as a conserved quantity as long as the forces involved are conservative. (en) Nella teoria dei sistemi dinamici, una costante del moto è una grandezza che resta invariata durante l'evoluzione del sistema. Dal punto di vista matematico si tratta dell'integrale primo dell'equazione del moto che descrive un sistema dinamico, cioè una funzione che rimane costante lungo le soluzioni di un problema differenziale. Nell'ambito della meccanica hamiltoniana, una costante del moto è una funzione che commuta con l'Hamiltoniana del sistema: dove in ambito classico il commutatore va sostituito con la parentesi di Poisson: (it) 在經典力學裏，對於一個動力系統，隨著時間的演進，所有保持不變的物理量都稱為守恆量（conserved quantity），又稱為運動常數。由於很多物理定律會表達某種守恆行為，對應的守恆量時常會出現於真實系統。例如，假設在某系統內涉及的作用力是保守力，則此系統的能量是守恆量。假設涉及的作用力是連心力，則此系統的角動量是守恆量。 (zh) |
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الكمية الثابتة في رياضيات النظام الديناميكي دالة للمتغيرات التابعة التي تظل قيمتها ثابتة على طول كل مسار للنظام. (ar) Nella teoria dei sistemi dinamici, una costante del moto è una grandezza che resta invariata durante l'evoluzione del sistema. Dal punto di vista matematico si tratta dell'integrale primo dell'equazione del moto che descrive un sistema dinamico, cioè una funzione che rimane costante lungo le soluzioni di un problema differenziale. Nell'ambito della meccanica hamiltoniana, una costante del moto è una funzione che commuta con l'Hamiltoniana del sistema: dove in ambito classico il commutatore va sostituito con la parentesi di Poisson: (it) 在經典力學裏，對於一個動力系統，隨著時間的演進，所有保持不變的物理量都稱為守恆量（conserved quantity），又稱為運動常數。由於很多物理定律會表達某種守恆行為，對應的守恆量時常會出現於真實系統。例如，假設在某系統內涉及的作用力是保守力，則此系統的能量是守恆量。假設涉及的作用力是連心力，則此系統的角動量是守恆量。 (zh) In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables, the value of which remains constant along each trajectory of the system. Not all systems have conserved quantities, and conserved quantities are not unique, since one can always produce another such quantity by applying a suitable function, such as adding a constant, to a conserved quantity. (en) |
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الكمية الثابتة (ar) Conserved quantity (en) Costante del moto (it) 守恆量 (zh) |
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