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.
Read more about Conserved Quantity: Differential Equations, Hamiltonian Mechanics, Lagrangian Mechanics
Famous quotes containing the word quantity:
“When we run over libraries persuaded of these principles, what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames; for it can contain nothing but sophistry and illusion.”
—David Hume (1711–1776)