- #1
Farina
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Before I get yelled at for cross-posting, it was advised that I post this query here, as opposed to the celestial mechanics forum.
PRE-QUESTION:
This questions pertains to celestial mechanics and
classical mechanics. Given that cross-posting is
frowned on -- what's a person to do to make sure
the both (appropriate) audiences are exposed to this post?
--------
Ok -
I have a particle moving in an inverse-cube force field.
One type of orbit for this particle is given by:
[tex]r=r_0 \cos \theta [/tex]
Apparently there are thus two additional types of
orbit possible.
What are their equations?
The only thing I can think of is that there are multiple
solution expressions (exponential form; sin, cos form, etc.
-- whatever the basic alternative forms are to solving 2nd order ODEs) to the governing differential equation for a particle moving in a central force field:
[tex]
\frac {d^2u}{d\theta^2} + u = -\frac {1}{ml^2u^2}f(u^{-1})
[/tex]
where:
u = 1/r
m = mass
l = angular momentum
[tex]f(u^{-1}) \text { = the central force} [/tex]
Other than remembering this stuff -- I'm at a loss
to see how to cough-up the other two orbit-type
equations.
Any ideas?
PRE-QUESTION:
This questions pertains to celestial mechanics and
classical mechanics. Given that cross-posting is
frowned on -- what's a person to do to make sure
the both (appropriate) audiences are exposed to this post?
--------
Ok -
I have a particle moving in an inverse-cube force field.
One type of orbit for this particle is given by:
[tex]r=r_0 \cos \theta [/tex]
Apparently there are thus two additional types of
orbit possible.
What are their equations?
The only thing I can think of is that there are multiple
solution expressions (exponential form; sin, cos form, etc.
-- whatever the basic alternative forms are to solving 2nd order ODEs) to the governing differential equation for a particle moving in a central force field:
[tex]
\frac {d^2u}{d\theta^2} + u = -\frac {1}{ml^2u^2}f(u^{-1})
[/tex]
where:
u = 1/r
m = mass
l = angular momentum
[tex]f(u^{-1}) \text { = the central force} [/tex]
Other than remembering this stuff -- I'm at a loss
to see how to cough-up the other two orbit-type
equations.
Any ideas?
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