Where did cotQ come from in canonical transformation?

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Discussion Overview

The discussion revolves around the origin of the term cotQ in the context of canonical transformations in classical mechanics. Participants are examining the mathematical expressions involved in these transformations and seeking clarification on specific derivations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant asks about the derivation of cotQ in the expression related to the generator of the transformation, specifically in the context of the function F(q,Q).
  • Another participant points out the need for the explicit generator of the transformation to understand the question fully.
  • A third participant clarifies that the function F is actually F=1/2*p*q and mentions that their original question was a remark related to an exercise.
  • One participant expresses their struggle with understanding classical mechanics, indicating a broader context of learning challenges.

Areas of Agreement / Disagreement

There is no consensus on the origin of cotQ, and multiple viewpoints regarding the need for clarity on the generator of the transformation remain. The discussion appears unresolved.

Contextual Notes

Participants have not provided all necessary details, such as the explicit generator of the transformation, which may limit understanding of the derivations discussed.

M. next
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I won't write the whole thing(unless asked for from you guys), but I just want to ask where did cotQ come from in canonical transformation.

For instance, F(q,Q) = 1/2p[itex]_{(q,Q)}[/itex]q => [itex]\partial[/itex]F/[itex]\partial[/itex]q=1/2p+1/2*[itex]\partial[/itex]p/[itex]\partial[/itex]q=1/2(p+qcotQ)=p.
What is this? How did the last things come from??
 
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How should we know, if you don't give the generator of the transformation explicitly?
 
Sorry my bad, I didn't know why this was important (if u may also clear that) but it is F=1/2*p*q, and this was at the end of an exercise, and what I posted in my original question, was a remark under the question! But I guess related to it
 
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I am struggling alone in understanding classical mechanics!
 

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