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Differential Form - Notation Help

  1. Jul 8, 2015 #1
    Hi there,

    I was reading up on Holonomic constraints and came across this equation on the Wikipedia page:

    fa14f9c440da57168334ebf30c88cf09.png

    The page says it is a differential form. Can anyone explain the notation for me or provide a link or two to documents or pages which explain this notation?

    Thank you very much,
    Geoff
     
  2. jcsd
  3. Jul 8, 2015 #2
    Cij = ∂fi/∂qj
    and
    Ci = ∂fi/∂t where fi is the i th constraint. and qj is the j th coordinate.
     
  4. Jul 8, 2015 #3

    lavinia

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    Science Advisor
    Gold Member

    You can interpret the dhqs and dt as small increments in the q's and in t.

    Formally a differential 1 form is a linear function on tangent vectors that varies smoothly from one tangent space to the next. .
     
  5. Jul 8, 2015 #4
    I'm quite confused.

    fa14f9c440da57168334ebf30c88cf09.png

    Why are there lower indices on the ##q^i##coordinate differentials?

    I would also expect to see an equal number of indeces on ##c##.
     
    Last edited: Jul 8, 2015
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