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vf321 Group Title

Is the following DE solvable? For constants m1, m2, and G, find the position vectors r1 and r2 as functions of time. We know: \[m_1\frac{d^2\vec r_1}{dt^2}=G\frac{m_1 m_2 (\vec r_1-\vec r_2)}{|\vec r_1-\vec r_2|^3}\]\[m_1\frac{d^2\vec r_1}{dt^2}=-m_2\frac{d^2\vec r_2}{dt^2}\]General solution with constants is preferred. If you're interested, this is the two-body problem.

  • 2 years ago
  • 2 years ago

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  1. vf321 Group Title
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    We also know that we are limited to planar motion, so we can look at four DEs: One for x1, y1, x2, y2.

    • 2 years ago
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    With\[\vec r_1=<x_1, y_1>\]and etc. for r2.

    • 2 years ago
  3. vf321 Group Title
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    ah forget it im going to math se.

    • 2 years ago
  4. vf321 Group Title
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    If any1's interested: http://math.stackexchange.com/questions/185593/solving-the-de-for-a-two-body-system

    • 2 years ago
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