Canonical and conjugate momentum

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    Conjugate Momentum
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SUMMARY

The discussion clarifies the distinction between canonical momentum and conjugate momentum in classical mechanics, specifically referencing the work of Goldstein. Canonical momentum, denoted as p, is defined as the derivative of the action with respect to the time derivative of a generalized coordinate q. The relationship {q,p}=1 indicates their conjugate nature, with the physical significance of p being contingent upon the interpretation of q.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with the concept of generalized coordinates
  • Knowledge of Hamiltonian mechanics
  • Basic grasp of action and Lagrangian formulations
NEXT STEPS
  • Study Hamiltonian mechanics and its applications
  • Explore the derivation of the action in classical mechanics
  • Learn about generalized coordinates and their significance
  • Investigate the implications of the Poisson bracket {q,p}=1
USEFUL FOR

This discussion is beneficial for physics students, educators, and researchers focusing on classical mechanics, particularly those interested in the mathematical foundations of Hamiltonian dynamics.

igraviton
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what is the difference between canonical and conjugate momentum.. ? what is its physical significant.. I was reading classical mechanics by Goldstein but could understood this terms
 
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Exactly the same thing. You might use the term conjugate momentum when you're referring to the canonical momentum which is conjugate to a particular coordinate.
 
Hi Bill_k,

Thanks for reply but what that means ? "conjugate to a particular coordinate"... physical intrepretation
 
The canonical conjugate momentum p is derived via a derivative of the action w.r.t. the time derivative of a generalized coordinate q. Then {q,p}=1. The physical interpretation of p depends on the interpretation of q.
 

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