What is the role of Conserved quantities in physical system?
Conservation of energy is the basis for the lossless harmonic oscillator equations, where the sum of potential energy V and kinetic energy T is a constant, and in the Hamiltonian, H = T + V.
In general conserved quantities are valuable because they are related to symmetries in the system being observed...Noether's Theorem. Some examples: momentum conservation is due to spacial symmetry, energy conservation is due to temporal symmetry, angular momentum conservation is due to parity symmetry.
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