How to convert 2nd order 2d equation to to first order

Asked Dec 23 '19 at 07:12

Active Dec 23 '19 at 07:12

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There is the equation for the gravity orbit:

 r' = v
 v' = -r/|r|^3

To solve it i need to convert to first order. It is clear that right side is the gradient:

grad(1/r) = -r/|r|^3

But for the cartesian it looks strange because of |r| and i am getting like:

rx' = vx
ry' = vy
vx' = -rx/|r|^3
vy' = -ry/|r|^3

asked Dec 23 '19 at 07:12

XMaSt3R

1

The equations you wrote are already of the first order (there is no double derivative) – Vasily Mitch Dec 23 '19 at 11:18
Note that $|r|$ is now the Euclidean norm of the vector $(r_x,r_y)$. – Lutz Lehmann Dec 23 '19 at 12:30

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