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Simultaneous differential equation of second order

  1. Nov 12, 2009 #1
    sorry for my English, i know its bad;)
    I have a simultaneous differential equation of second order (moving of point mass around point mass M in beginning of cartesian system)
    [tex]\begin{cases}\frac{\mbox{d}^2x}{\mbox{d}t^2}=-GMx\left(x^2+y^2\right)^{-\frac{3}{2}}\\ \frac{\mbox{d}^2y}{\mbox{d}t^2}=-GMy\left(x^2+y^2\right)^{-\frac{3}{2}}\end{cases}[/tex]
    and I need to find how x and y changes depending on t.
    solving by substitution takes very long time, so other method which allows to solve it in shorter and more simply way would be appreciated;)
    i am not sure if this thread is good for this topic, please move it if its bad location
    thanks for your help;)
  2. jcsd
  3. Nov 12, 2009 #2


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    Newton solved those equations in polar coordinates. I have never seen them solved in Cartesian coordinates.
  4. Nov 13, 2009 #3
    yeah, i came to it that it must be in polar system, i solved it and everything is good:)
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