How can I use Poisson bracket to find P in a canonical transformation?

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SUMMARY

The discussion focuses on using the Poisson bracket to determine the variable P in a canonical transformation where q and p transform to Q and P. The transformation is defined as Q = q(t+s) + (t+s)p, with the Poisson bracket {Q,P}qp set to 1. The solution involves manipulating the Poisson bracket definition to derive the relationship between P and the variables involved.

PREREQUISITES
  • Understanding of canonical transformations in Hamiltonian mechanics
  • Familiarity with Poisson brackets and their properties
  • Knowledge of differential calculus, particularly partial derivatives
  • Basic grasp of classical mechanics concepts
NEXT STEPS
  • Study the properties of Poisson brackets in detail
  • Explore canonical transformations and their applications in Hamiltonian mechanics
  • Learn about the implications of the Hamiltonian equations of motion
  • Investigate examples of transformations in classical mechanics
USEFUL FOR

This discussion is beneficial for students and researchers in physics, particularly those focusing on classical mechanics and Hamiltonian systems, as well as anyone looking to deepen their understanding of canonical transformations and Poisson brackets.

Apashanka das
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Homework Statement


q,p transforms canonicaly to Q,P where given Q=q(t+s)+(t+s)p ,t is time and s is constt
To find P

Homework Equations


Poisson bracket {Q,P}qp=1

The Attempt at a Solution


Using Poisson bracket I find (t+s)*(dP/dp-dP/dq)=1
 
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Start with the definition of a Poisson bracket.
 

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