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In mathematics, a conserved quantity of a dynamical system is a function H of the dependent variables that is a constant (in other words, conserved) along each trajectory of the system. A conserved quantity can be a useful tool for qualitative analysis. Not all systems have conserved quantities, however the existence has nothing to do with linearity (a simplifying trait in a system) which means that finding and examining conserved quantities can be useful in understanding nonlinear systems. Conserved quantities are not unique, since one can always add a constant to a conserved quantity.

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  • Conserved quantity
  • Costante del moto
  • 守恆量
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  • 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:
  • 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。
  • In mathematics, a conserved quantity of a dynamical system is a function H of the dependent variables that is a constant (in other words, conserved) along each trajectory of the system. A conserved quantity can be a useful tool for qualitative analysis. Not all systems have conserved quantities, however the existence has nothing to do with linearity (a simplifying trait in a system) which means that finding and examining conserved quantities can be useful in understanding nonlinear systems. Conserved quantities are not unique, since one can always add a constant to a conserved quantity.
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  • In mathematics, a conserved quantity of a dynamical system is a function H of the dependent variables that is a constant (in other words, conserved) along each trajectory of the system. A conserved quantity can be a useful tool for qualitative analysis. Not all systems have conserved quantities, however the existence has nothing to do with linearity (a simplifying trait in a system) which means that finding and examining conserved quantities can be useful in understanding nonlinear systems. Conserved quantities are not unique, since one can always add a constant to a conserved quantity. Since most laws of physics express some kind of conservation, conserved quantities commonly exist in mathematic models of real systems. For example, any classical mechanics model will have energy as a conserved quantity so long as the forces involved are conservative.
  • 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:
  • 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。
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