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Geodesic equation

  1. May 16, 2005 #1
    I don't understand the equation of the geodesic y=y(x) for the surface given by z=f(x,y) :

    [tex] a(x)y''(x)=b(x)y'(x)^3+c(x)y'(x)^2+d(x)dxdy-e(x) [/tex]

    the functions a,b,c,d,e are here not very important, what I dont understand, is that there is terms in [tex]\frac{dy}{dx}[/tex] and [tex]dxdy[/tex].....What does this mean ?
     
  2. jcsd
  3. May 17, 2005 #2

    dextercioby

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    Where did you get that equation...?It should come from the tensor one involving Christoffel symbols.

    Daniel.
     
  4. May 17, 2005 #3
    This is the equation in the special case where z=f(x,y)...the geodesics being given in the direct form : y=y(x)....I got this in Bronstein Taschenbuch der Mathematik.
     
  5. May 17, 2005 #4

    dextercioby

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    I'm sorry,i can't get that book.Could u please indicate other source (it would be sizzling,if online) ?

    Daniel.
     
  6. May 18, 2005 #5
    Here is a scan :
     

    Attached Files:

  7. May 18, 2005 #6

    dextercioby

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    It's a typo,i'm sure the German dude meant the derivative of the first order

    [tex] \frac{dy}{dx} [/tex].

    Daniel.
     
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