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vf321
 3 years ago
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 twobody problem.
vf321
 3 years ago
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 twobody problem.

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vf321
 3 years ago
Best ResponseYou've already chosen the best response.0We also know that we are limited to planar motion, so we can look at four DEs: One for x1, y1, x2, y2.

vf321
 3 years ago
Best ResponseYou've already chosen the best response.0With\[\vec r_1=<x_1, y_1>\]and etc. for r2.

vf321
 3 years ago
Best ResponseYou've already chosen the best response.0ah forget it im going to math se.

vf321
 3 years ago
Best ResponseYou've already chosen the best response.0If any1's interested: http://math.stackexchange.com/questions/185593/solvingthedeforatwobodysystem
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