Extended Gauss' propagator

[jorgepiloto]

I took directly the algorithm from Battin 1999, section 5.6 and tested the algorithm with the proposed example 5-30.

This algorithm still needs to be finished, so CI is going to fail. But I decided to make the PR just for receive code reviews and keep working on this. Last part of Battin's explanation about the algorithm is a little bit confusing.

This may solve when finished #475

[astrojuanlu]

As you requested a review, I left some early comments

[astrojuanlu]

Is there a chance we have the derivative of the function? I think the answer is yes, so I would use newton instead. Even if we don't provide the derivative, I would not use root, because it's too general purpose and impossible to accelerate with numba (unless we explore #486)

[jorgepiloto]

I've decided to work again on this since I have some free time today. However, even if the tests pass some things still need to be done:

• When the algorithm checks if the value of A is higher than A_m and gets inside the conditional, the returned orbit is propagated wrong. I have spent hours checking and debugging and not sure if this part is well implemented in the code. Still working on this

• Furthermore, some docstings are needed

What a pity Riot-Matrix is down today 😢

[codecov]

Codecov Report

Merging #631 into master will decrease coverage by 2.88%.
The diff coverage is 67.81%.

@@            Coverage Diff             @@
##           master     #631      +/-   ##
==========================================
- Coverage   87.17%   84.28%   -2.89%     
==========================================
  Files          52       51       -1     
  Lines        2580     2533      -47     
  Branches      220      198      -22     
==========================================
- Hits         2249     2135     -114     
- Misses        262      344      +82     
+ Partials       69       54      -15

Impacted Files	Coverage Δ
src/poliastro/twobody/propagation.py	79.72% <67.81%> (-16.7%)	⬇️
src/poliastro/plotting/porkchop.py	0% <0%> (-75.44%)	⬇️
src/poliastro/core/iod.py	74.85% <0%> (-13.78%)	⬇️
src/poliastro/frames.py	71.42% <0%> (-6.73%)	⬇️
src/poliastro/core/elements.py	93.33% <0%> (-6.67%)	⬇️
src/poliastro/twobody/orbit.py	88.99% <0%> (-1.61%)	⬇️
src/poliastro/maneuver.py	94.44% <0%> (-0.16%)	⬇️
src/poliastro/threebody/soi.py	100% <0%> (ø)	⬆️
src/poliastro/plotting/static.py	87.37% <0%> (ø)	⬆️
src/poliastro/czml/czml_extract_default_params.py
... and 4 more

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update ec2dc04...4f540b1. Read the comment docs.

[astrojuanlu]

Pending:

• Rebase on current master
• Add failing tests
• Add link to paper that contains full flow chart

[jorgepiloto]

Link to paper on Gauss Algorithm: https://dspace.mit.edu/handle/1721.1/16383

[jorgepiloto]

This is going to be my priority during the following days. I will read in detail the paper because even that if Battin is the advisor, I am not sure if it is the same algorithm that the one explained on his book.
And as it is said in the introduction to the paper:

The final algorithm is a general form valid for any orbit of any eccentricity and requires no knowledge of the nature of tKo orbit for application.

So this is supposed to be what I call the MOAP (Mother Of All Propagators) 😆

[jorgepiloto]

Current status of this algorithm:

• There are two implemented tests: one is from Battin (passing) and another one that tests all the propagators in poliastro (failing in gauss).

• Algorithm works well if not entering in the elif section, that means that A never exceeds A_max = 0.3. Otherwise algorithm does not converge well. I have done line by line debugging but everything looks good when executing different parts of the code. Problem may be located at this section but I am not able to find the bug.

• Notice that on the failing tests, results just diverge from a few km.

[jorgepiloto]

Current status and updates on this pull request:

• After Fix near parabolic regimes #908 and Refactor propagators #918 this algorithm interest has become just "archeological". As other Kepler routines, this might be interesting for comparison purposes.

• ⚠️ Just found the original paper for the algorithm with DOI: https://doi.org/10.2514/3.55860
  This might lead to the final implementation of this solver.