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What does this two momentum transform look like?

  1. Aug 25, 2015 #1
    qi is the cartesian coordinate, and Qi is the Generalized coordinate, why the momentum under the two coordinates have this transformation way:
    pi=∑Pj(∂Qj/∂qj)
    pi and Pi are corresponding momentum under the two coordinate respectively.
     
  2. jcsd
  3. Aug 25, 2015 #2

    DEvens

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    Hi rtransformation. Welcome to the forum.

    This is how vectors transform under a coordinate transformation. You need to study vector transformations. For example, rotations, changes to spherical or cylindrical coordinates, etc.

    So the reason that momentum transforms this way is that it is a vector.
     
  4. Aug 25, 2015 #3
    Thank you! I really need to study some basic knowledge now...Thank you again.
     
  5. Aug 25, 2015 #4
    actually, I didn't find the relation between the vector transformation and my question, could you please be more specific and help me solve this problem?Thank you very much.
    Is this transformation a contact transformation?
     
    Last edited: Aug 25, 2015
  6. Aug 25, 2015 #5

    DEvens

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    I have no idea if it is a "contact transformation." I looked up "contact transformation."

    https://en.wikipedia.org/wiki/Contact_geometry

    It was fun, but seemed to be somewhat far afield from your question.

    What sort of answer would satisfy you? This is how a vector transforms under a coordinate change. It is part of the definition of a vector.
     
  7. Aug 25, 2015 #6
    I just want to know how I can get this result through derivation.:frown:
     
  8. Aug 25, 2015 #7
    I would suggest looking at a graduate level classical mechanics book in a chapter on canonical transformations.
     
    Last edited: Aug 25, 2015
  9. Aug 25, 2015 #8
    Thank you, I now get it.
     
  10. Aug 26, 2015 #9
    I'm not sure I do though. Would you mind posting your explanation for the curious reader?
     
  11. Aug 27, 2015 #10
    I found it in the Walter Greiner‘s famous classical mechanics book “Classical Mechanics——Systems of Particles and Hamiltonian Dynamics” ,Chapter 19——Canonical Transformation,and what I asked is the point transformation which is discussed in detail in this book.
     
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