Canonical and conjugate momentum

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Canonical momentum and conjugate momentum are often used interchangeably, but they have distinct meanings in classical mechanics. Canonical momentum is defined as the derivative of the action with respect to the time derivative of a generalized coordinate, while conjugate momentum specifically refers to the momentum associated with a particular coordinate. The relationship between generalized coordinates and their conjugate momenta is expressed through the Poisson bracket, where {q,p}=1. The physical significance of canonical momentum depends on the interpretation of the corresponding generalized coordinate. Understanding these concepts is crucial for grasping the foundations of classical mechanics.
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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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