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
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