Added recursive series Kepler solver for elliptical orbits #1439

JackCrusoe47 · 2022-01-14T12:45:16Z

Added the series solution approximation for elliptical orbits. $(E\approx M e \sin( M \cdots e \sin(M)) \cdots )$
Small correction to Danby code. Corrected nu to M for circular orbits as M = nu @ e=0

Currently, I only included the manual series solution, where the user provides the order of recursion (instead of tolerance).

Later, I can implement a hybrid variant that uses a lookup table to select appropriate order for a mean anomaly and eccentricity and then uses the initial guess for a Newton-Raphson. Here, the user will be able to specify a tolerance, and hopefully, the table provides an order of recursion that overall reduce the cost of computing the solution. I am currently having trouble with fast lookup.

Hope I didn't mess anything up with the pull request. I have never worked with Github.

Cheers

Recursive series solution solver for elliptical Kepler's problem.

Added recSeries solver to propagation __init__ file.

Performed clean up corrections to the recursive solver * removed numiter options were left in the previous commit

Corrected to simply the nu_to_M case for circular orbit (M=E=nu @ e=0)

for more information, see https://pre-commit.ci

codecov · 2022-01-14T13:14:53Z

Codecov Report

Merging #1439 (b5b30f3) into main (9797eb0) will decrease coverage by 0.07%.
The diff coverage is 84.44%.

@@            Coverage Diff             @@
##             main    #1439      +/-   ##
==========================================
- Coverage   91.93%   91.85%   -0.08%     
==========================================
  Files          93       94       +1     
  Lines        4400     4444      +44     
  Branches      422      429       +7     
==========================================
+ Hits         4045     4082      +37     
- Misses        267      272       +5     
- Partials       88       90       +2

Impacted Files	Coverage Δ
src/poliastro/core/propagation/recseries.py	`80.55% <80.55%> (ø)`
src/poliastro/core/propagation/__init__.py	`100.00% <100.00%> (ø)`
src/poliastro/core/propagation/danby.py	`96.49% <100.00%> (ø)`
src/poliastro/twobody/propagation.py	`92.30% <100.00%> (+0.55%)`	⬆️

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astrojuanlu

Amazing @JackCrusoe47 ! That's what I call "from zero to hero" 😃 Good use of GitHub, nothing to worry about there.

I have a few minor requests:

Could you rename the module and function names to all_lowercase instead of camelCase? to keep consistency
Could you add your method here

poliastro/src/poliastro/twobody/propagation.py

Lines 488 to 497 in 9797eb0

    
           ELLIPTIC_PROPAGATORS = [ 
        
               farnocchia, 
        
               vallado, 
        
               mikkola, 
        
               markley, 
        
               pimienta, 
        
               gooding, 
        
               danby, 
        
               cowell, 
        
           ]

so it gets tested automatically?

JackCrusoe47 · 2022-01-14T15:21:40Z

Thank you @astrojuanlu.

of course, I'll do the corrections right away. I also saw that two automatic tests are failing. Is it related to not adding my method in the tests, or would I need to modify anything further?

The tests that fail are:

codecov/patch
codecov/project

-Updated solver name to be more in line with project guidelines. -Updated zero-order solution to E = M+e (Vallado) for improved convergence

Yash-10 · 2022-01-14T15:25:31Z

Wow! This seems to be a great addition. As the paper states,

Fast approximation of closest approach distance for co-planar orbits.

this approach could also be a good approach to check out for the satellite collision event #1350, isn't it?

for more information, see https://pre-commit.ci

Updated solver name to better be in line with project guidelines

Added recursive series propagator for elliptical Keplerian problem.

for more information, see https://pre-commit.ci

Correction

Corrected esle to else

for more information, see https://pre-commit.ci

Further spell errors and function names

JackCrusoe47 · 2022-01-14T16:30:14Z

@Yash-10 A possible method could be to use recursive series to do a fast estimation. Then once a potential collision region is identified, more accurate methods like Newton-Raphson computes the precise distance and location.

P.S I apologize about the state of my commits. I still have not found a way to roll back my commits.

fixed iteration method. tolerance for a given order varies for different M and ecc values.

Tolerance from given order computation. Very approximate, but good for low to mid tolerance values and low eccentricities order = 2 * floor( - log10( tolerance ) )

for more information, see https://pre-commit.ci

astrojuanlu

5 tests have failed:

FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.9]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.99]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.999]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.9999]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.99999]

which means that, with eccentricities of 0.9 and higher, the method loses a bit of accuracy.

I assume this is how the method works, so I'll assist you in relaxing the tolerance for the tests without affecting the other methods.

JackCrusoe47 · 2022-01-14T18:14:01Z

5 tests have failed:
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.9]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.99]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.999]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.9999]
FAILED tests/tests_twobody/test_propagation.py::test_elliptic_near_parabolic[recseries-0.99999]
which means that, with eccentricities of 0.9 and higher, the method loses a bit of accuracy.

I assume this is how the method works, so I'll assist you in relaxing the tolerance for the tests without affecting the other methods.

Unfortunately yes. The rate of convergence of the method drops to zero as the eccentricity becomes close to 1. In theory, it should work for cases up to 0.99 with a high enough order (say 20-30 for 0.99 for example). But for now the function I use to convert accuracy to order probably is underpredicting the order for 0.9 and 0.99.

JackCrusoe47 · 2022-01-14T18:22:57Z

Well, I can make it work with a fixed tolerance instead of fixed recursion order. By adding three functions inside recseries.py

recseries_coe_order (user-specified order)
recseries_coe_rtol (user-specified rtol)
recseries (general solver able to work with both types)

Compute eccentricity for recseries propagation Updated rtol to order function

for more information, see https://pre-commit.ci

removed extra order = order =

Added ability to choose two different methods of series recursion termination - fixed user-defined order as method='order' - fixed user-defined tolerance as method='rtol'

for more information, see https://pre-commit.ci

run recseries through user-specified tolerance

for more information, see https://pre-commit.ci

Correction: [recseries_fast(k, r0, v0, tof, method='rtol', order=8, numiter=100, rtol) for tof in tofs]

Correction recseries call

for more information, see https://pre-commit.ci

JackCrusoe47 · 2022-01-14T19:57:45Z

All cases more or less should work now.

Now the recseries( ) solver can be called in the following two ways:

(rf,vf) = recseries(k, r0, v0, tof, method='order', order=12) # use a fixed 12th order recursive series
(rf,vf) = recseries(k, r0, v0, tof, method='rtol', rtol=1e-8) # recurse until a tolerance of 1e-8

This works the same for recseries_coe( )

astrojuanlu

Looks good to me! Will merge when the tests pass 💪🏼

JackCrusoe47 · 2022-01-14T20:06:31Z

Perfect. Thank you.

astrojuanlu · 2022-01-14T21:38:06Z

A small coverage difference is not worth blocking this PR 😉

astrojuanlu · 2022-01-14T21:38:34Z

Congratulations @JackCrusoe47 on your first contribution to poliastro! 🎉

JackCrusoe47 · 2022-01-15T03:00:52Z

Thank you @astrojuanlu for merging my commits 🚀. I am eager to see its use by the community. 😄

JackCrusoe47 and others added 5 commits January 14, 2022 17:23

Create recSeries.py

f70d862

Recursive series solution solver for elliptical Kepler's problem.

Updated __init__.py with recSeries solver

3fb3896

Added recSeries solver to propagation __init__ file.

Corrections and Comments

8947bef

Performed clean up corrections to the recursive solver * removed numiter options were left in the previous commit

Slight correction on nu_to_M for circular orbits

d0735ee

Corrected to simply the nu_to_M case for circular orbit (M=E=nu @ e=0)

[pre-commit.ci] auto fixes from pre-commit.com hooks

f715a38

for more information, see https://pre-commit.ci

astrojuanlu suggested changes Jan 14, 2022

View reviewed changes

Updated the propagator name to recseries

66bac2f

-Updated solver name to be more in line with project guidelines. -Updated zero-order solution to E = M+e (Vallado) for improved convergence

pre-commit-ci bot and others added 8 commits January 14, 2022 15:25

[pre-commit.ci] auto fixes from pre-commit.com hooks

7862250

for more information, see https://pre-commit.ci

Updated solver name to recseries from recSeries

092094a

Updated solver name to better be in line with project guidelines

Added recseries propagator for elliptical orbits

92b87ff

Added recursive series propagator for elliptical Keplerian problem.

[pre-commit.ci] auto fixes from pre-commit.com hooks

2f2353b

for more information, see https://pre-commit.ci

Correction recseries

554e2c1

Correction

Correction miss-spelled else

91141d2

Corrected esle to else

[pre-commit.ci] auto fixes from pre-commit.com hooks

5be4ab0

for more information, see https://pre-commit.ci

Corrected eccentricity e and name

b52f7b6

Further spell errors and function names

JackCrusoe47 and others added 3 commits January 14, 2022 22:22

removed order dependence on rtol

759886d

fixed iteration method. tolerance for a given order varies for different M and ecc values.

Simple order from tolerance computation

71ecbd1

Tolerance from given order computation. Very approximate, but good for low to mid tolerance values and low eccentricities order = 2 * floor( - log10( tolerance ) )

[pre-commit.ci] auto fixes from pre-commit.com hooks

fd2e83e

for more information, see https://pre-commit.ci

JackCrusoe47 requested a review from astrojuanlu January 14, 2022 17:59

astrojuanlu reviewed Jan 14, 2022

View reviewed changes

JackCrusoe47 and others added 4 commits January 15, 2022 00:04

Updated rtol to order function

1781f9d

Compute eccentricity for recseries propagation Updated rtol to order function

[pre-commit.ci] auto fixes from pre-commit.com hooks

c1f23ca

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error correction

51275ae

removed extra order = order =

overhauled recseries.py

dcd0d9d

Added ability to choose two different methods of series recursion termination - fixed user-defined order as method='order' - fixed user-defined tolerance as method='rtol'

pre-commit-ci bot and others added 6 commits January 14, 2022 19:31

[pre-commit.ci] auto fixes from pre-commit.com hooks

df0a86e

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updated recseries propagation

de49c28

run recseries through user-specified tolerance

[pre-commit.ci] auto fixes from pre-commit.com hooks

d1d70f1

for more information, see https://pre-commit.ci

Corrected recseries call signature

32cb08c

Correction: [recseries_fast(k, r0, v0, tof, method='rtol', order=8, numiter=100, rtol) for tof in tofs]

Correction recseries

65a3374

Correction recseries call

[pre-commit.ci] auto fixes from pre-commit.com hooks

b5b30f3

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astrojuanlu approved these changes Jan 14, 2022

View reviewed changes

astrojuanlu enabled auto-merge January 14, 2022 20:05

astrojuanlu disabled auto-merge January 14, 2022 21:38

astrojuanlu merged commit 7685305 into poliastro:main Jan 14, 2022

JackCrusoe47 deleted the add_recSeries branch January 15, 2022 03:01

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Added recursive series Kepler solver for elliptical orbits #1439

Added recursive series Kepler solver for elliptical orbits #1439

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	ELLIPTIC_PROPAGATORS = [
	farnocchia,
	vallado,
	mikkola,
	markley,
	pimienta,
	gooding,
	danby,
	cowell,
	]

Added recursive series Kepler solver for elliptical orbits #1439

Added recursive series Kepler solver for elliptical orbits #1439

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