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National Bird Day: Why Birds Matter to Us

National Bird Day is celebrated every year on 5 January . This day is observed to spread awareness about birds, their importance in nature, and the need to protect them. Birds are beautiful living beings and play a very important role in keeping our environment healthy. Origin of National Bird Day National Bird Day was first celebrated in the year 2002 . It was started by bird lovers and environmental groups to protect birds from dangers like deforestation, pollution, and illegal hunting. The main aim of this day is to teach people, especially students, why birds are important and how we can help save them. Why Is National Bird Day Celebrated Every Year? National Bird Day is celebrated every year because many bird species are disappearing due to human activities. Cutting trees, using plastic, pollution, and climate change are harming birds and their homes. This day reminds us that: Birds need protection Nature should be respected Everyone has a responsibil...
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Jacobi-Poisson theorem | Poisson’s second theorem | Classical mechanics

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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