OHM Lagrange MFD

[ADSWNJ]

Latest update on this project:

The alpha test crew and I are working through a couple of alpha releases a week, gradually tuning things ready for you guys to play with. The underlying physics engine is working very nicely, calculating non-Keplerian orbits and insanely interesting resonant encounters going through multiple Lagrange Points. The burn engine is looking good. We need more work on the Station Keeping engine, and some work on the graphics, and then it'll be good enough for a V1 release.

 

[IronRain]

I'm _really_ looking forward to this one. Keep up the great work guys!

 

[jgrillo2002]

Sounds good. Take your time with this, as patience has great rewards and less bugs.

 

[dgatsoulis]

Here is a small teaser of the new Lagrange MFD in action. The video's purpose was bug reporting between the testing team, but I got the ok to share with the rest of the community.

An EML1 to EML2 transfer using the new Lagrange MFD.

 

[ADSWNJ]

Check out the amazing non-Keplerian orbit at 01:00 (green line), oscillating between EML1, the Moon, and EML2. Not only do we calculate the encounter three flips round the Moon, but we execute a highly precise burn and track to the target.

Go team!!

 

[Enjo]

Andrew and the Team, I admire your motivation

 

[Ajaja]

Very interesting! Could you compare stability of calculated orbits with my old module?
[ame="http://www.orbithangar.com/searchid.php?ID=4582"]Lagrangian points MFD v0.2[/ame]

 

[Keithth G]

Hi, 'Ajaja'

What is the underlying physical theory of your Lagrange points MFD? Is it CR3BP or the ER3BP? ASDWNJ's Lagrange MFD is based on the latter.

From experience, I know that if placed at L1 or L2 of the Earth-Moon system in Lagrange MFD, a vessel will noticeably drift off onto the unstable manifold in around 10 days.

 

[Ajaja]

I used
https://map.gsfc.nasa.gov/ContentMedia/lagrange.pdf
equations (10), (11)

 

[Keithth G]

I used
https://map.gsfc.nasa.gov/ContentMedia/lagrange.pdf
equations (10), (11)

Thanks, 'Ajaja'

Equation (10) gives the standard fifth-order polynomial for 'u' (to use the paper's notation). This polynomial equation is actually valid for both the circular and elliptic three-body theories of Lagrange points - although the paper deals with the former, and not the later.

The difference between the circular theory and elliptic theory is that the former assumes that the Moon moves around the Earth in a circle; whereas the latter assumes that the Moon orbits the Earth in an ellipse.

Equation (11) gives the first-order expansion for the position of the collinear Lagrange points for the circular theory (fixed 'R'). For the Earth-Moon system, the expansion parameter ([math]\alpha^{1/3} [/math]) is around 0.23 - so, in practice, one really needs a considerably higher-order expansion to get a good handle on the location of the Lagrange points.

In Lagrange MFD (ADSWNJ's version), the quintic is solved directly to calculate the location of the Lagrange points - although we have worked out expansion schemes up to 30th order in the parameter [math]\alpha^{1/3} [/math]; it uses the elliptic version of the three-body theory so it uses a better model of the motion of the Moon; and for Earth-Moon L4/L5, it also introduces a factor to compensate for the torquing of the Moon's orbital plane by gravitational tidal forces exerted by the Sun.

On the whole, we find that if we place a Vessel at a collinear Lagrange point (with the right speed of course), then it may take upwards of a day for the Vessel to move more than a few metres from the Lagrange point.

 

[Ajaja]

Eq.(10) gives good stability, but not enough:

http://orbiter-forum.com/showthread.php?p=127798
Moon L1:

I have ~1.2M shift from L1 ater 14 days (3.8days-1k, 7.3 - 10k, 10.6-100k, 13.8-1000k).

So I'm curious about ADSWNJ's results.

 

[Keithth G]

Eq.(10) gives good stability, but not enough:

http://orbiter-forum.com/showthread.php?p=127798
Moon L1:


So I'm curious about ADSWNJ's results.

I've just run this scenario through ADSWNJ's Lagrange MFD for an arbitrary date and this is what I get for EML1:

Day 0 0.007 km
Day 1 0.048 km
Day 2 0.093 km
Day 3 0.033 km
Day 4 0.176 km
Day 5 0.445 km
Day 6 0.706 km
Day 7 1.105 km
Day 8 1.994 km
Day 9 3.654 km
Day 10 6.462 km
Day 11 11.433 km
Day 12 20.919 km
Day 13 39.362 km
Day 14 75.598 km

I suspect that these results are fairly indicative of other dates

 

[Ajaja]

Thanks. Amazing, 75 km after 14 days - excellent result!!! Looking forward to release of the MFD

 

[Ajaja]

BTW, what's happened with 'Keithth G' posts? Forum glitch?

 

[boogabooga]

BTW, what's happened with 'Keithth G' posts? Forum glitch?

ALL of 'Keithth's posts were edited (to deletion) over a finite period of time a few days ago. Also, the Youtube channel was closed.

It seems that Keithth proactively spent time to make his online presence disappear. :shifty:

A real shame to loose a brilliant forum member like that. Hope he is alright.

 

[Enjo]

Not good...

 

[Urwumpe]

Not good...

Not sure. I have seen too much here to be automatically concerned.

 

[MikeB]

ALL of 'Keithth's posts were edited (to deletion) . . .

I hope his work isn't permanently gone. One of my back-burner projects has been to edit and post his work to the Rocket Science For Amateurs section of OrbiterWiki. Of course, I haven't been saving his posts as they came up, assuming I could get them whenever I wanted.

 

[ADSWNJ]

I can confirm the Lagrange team has also lost contact with Keith. I'm still committed to completing the project and getting this MFD released, but it's with a heavy heart, as this was Keith's brainchild.

Keith - if you are still monitoring this, please let me know all is good and you just want a break from things. If you need anything, please reach out. Miss you, brother.

 

[Face]

It seems that Keithth proactively spent time to make his online presence disappear. :shifty:

Sounds like either somebody seriously pissed him off here, or some weird license/patent lawyer .

Whatever it is, give him some rest to sort it out.