Jacobi-Poisson theorem Poisson’s second theorem If u and v are any two constants of motion of any given system, then their Poisson bracket [ u , v ] are also a constant of motion. If u is a constants of motion, then [ u , H ] + ∂ u /∂t = 0 ⇒ [ u , H ] = - ∂ u /∂t. Given u and v are constant of motion We have to prove [u, v] is also a constant of motion Proof By Jacobi identity This is mathematical form of Jacobi-Poisson’s theorem or Poisson's second theorem . According to statement of Jacobi-Poisson theorem if u and v are any two constants of motion of any given system, then their Poisson bracket [ u , v ] are also a constant of motion. To know about Jacobi-Poisson theorem of Poisson second theorem click on the link for English and click on the link for Hindi...
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