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[Orekit Developers] status on second order derivatives


As some of you may be aware, I have been working for a few months on second order derivatives in the git branch position-velocity-acceleration. This work is still ongoing but I hope to finish it for 7.0 and merge the branch back to master soon. For now, there are still failing tests so I can't do it.

This change should allow us to reach several goals :

 - improved accuracy in shiftedBy methods
 - improved accuracy in interpolators (with user-defined
   choices to use or not first and second derivatives
   from the sample)
 - improved accuracy in attitude
 - removal of ugly hidden finite differences in some classes
   (most notably attitude modes) with hard-coded steps
 - hopefully faster Earth transforms, by replacing Hermite
   interpolation with single point extrapolation
 - availability of non-Keplerian acceleration everywhere
 - availability of angular acceleration in attitude and frames
 - proper composition of dynamics in frames
 - possibility to propagate orbits in non-inertial frames
 - possibility to propagate orbits without a central body
   (interplanetary missions, Lagrange point missions, ...)

There is one point that bothers me right now. As I removed some of the ugly finite differences, some non-regression tests started to fail. I finally found the raw cause of these failures and was surprised to discover an old bug in the way we use the osculating orbits produced by the Eckstein-Hechler analytical propagator. This propagator takes zonal terms into account, and produces directly circular parameters a, ex, ey, ... When we compute anything related to geometry, we compute Cartesian coordinates using the Orbit getPVCoordinates method. As the Orbit classes do not know anything about the perturbation, the (P, V) pair does in fact implicitly relies on Keplerian-only expressions. So the velocity part is *not* consistent with the derivative of the position. The real derivative of the position takes the non-Keplerian effects into account which are ignored by getPVCoordinates. The difference is small, but as the tests threshold were deliberatly very tight, the tests started to fail when the various pointing directions were not computed anymore from finite differences mainly involving position and when they relied on the computed velocity. So the problem already happens in the master branch, it is not specific to the introduction of acceleration (it was just detected here during testing).

The solution is in fact quite simple. If an orbit has been produced by a non-Keplerian propagator, the propagator already knows about the derivatives of the orbital elements (which are circular in the Eckstein-Hechler model case but can be any kind of parameters for other propagators). The propagator should therefore provide these derivatives to the orbit so they can be used in the PVCoordinates conversion. The code is very simple and straightforward. I have checked this and got very interesting results with Eckstein-Hechler/Circular, as for example a simple interpolation over a 900s arc with proper velocity/acceleration has a 88m error with two base points now whereas it was 5162 m before (and 0.02m vs 650m for 3 points, 1.0e-5m vs 259m for 4 points).

Here is what bothers me:

Should we create specialized classes for perturbed orbits or should we simply add a constructor to the existing orbits with the parameters derivatives and set them to 0 when they are not known?

For my tests, I created PerturbedCircularOrbit which extends CircularOrbit and override the protected initPVCoordinates method and the public shiftedBy and interpolate methods. I could also have simply moved everything into CircularOrbit with a new constructor.

I do not like much the PerturbedXxxxOrbit approach, as it forces to create also additional entries in the OrbitType enum with additional converters and it becomes awkward if for example a user configures a NumericalPropagator to generate XxxxOrbit, despite this propagator will in fact really generate PerturbedXxxOrbit because it is what a Numerical propagator is for. So there should be either an internal modification of the user setting from OrbitType.XXXX to OrbitType.PERTURBED_XXXX or an error triggered which would invalidate *all* current user code as it would become forbiddent to generate XXXX orbits now.

On the other hand, the drawback of modifying the existing classes to hold the non-Keplerian derivatives is that they will consume more memory. I don't think it is a problem with current computers.

In any case, initial orbits created directly from user code or by reading files would not include the derivatives and therefore will be built as usual (by calling the unmodified classes in the first approach, or by using the already existing constructors in the second approach, assuming these constructors will automatically set the derivatives to Keplerian-only values). In any case, full-blown perturbed orbits will be created internally by Orekit propagators, which can easily be modified to provide the derivatives they know (by creating instances of the new derived classes in the first approach, or by using new constructors with additional parameters in the second approach).

My humble opinion would be to use the second approach to solve this bug. I will probably do this in the position-velocity-acceleration branch so it will include accelerations right from the start and will be merged to master at the same time as the rest of the branch. Of course, this will be a dedicated commits (Git branches are great!).

What do you think ?

best regards,

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